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1
Kamenetsky, Dmitry, and dkamen@rsise anu edu au. "Ising Graphical Model." The Australian National University. ANU College of Engineering and Computer Science, 2010. http://thesis.anu.edu.au./public/adt-ANU20100727.221031.
Анотація:
The Ising model is an important model in statistical physics, with over 10,000 papers published on the topic. This model assumes binary variables and only local pairwise interactions between neighbouring nodes. Inference for the general Ising model is NP-hard; this includes tasks such as calculating the partition function, finding a lowest-energy (ground) state and computing marginal probabilities. Past approaches have proceeded by working with classes of tractable Ising models, such as Ising models defined on a planar graph. For such models, the partition function and ground state can be computed exactly in polynomial time by establishing a correspondence with perfect matchings in a related graph.
In this thesis we continue this line of research. In particular we simplify previous inference algorithms for the planar Ising model. The key to our construction is the complementary correspondence between graph cuts of the model graph and perfect matchings of its expanded dual. We show that our exact algorithms are effective and efficient on a number of real-world machine learning problems. We also investigate heuristic methods for approximating ground states of non-planar Ising models. We show that in this setting our approximative algorithms are superior than current state-of-the-art methods.
2
Li, Chengshu. "Tricritical Ising edge modes in a Majorana-Ising ladder." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62467.
Анотація:
While Majorana fermions remain at large as fundamental particles, they emerge in condensed matter systems with peculiar properties. Grover et al. proposed a Majorana-Ising chain model, or the GSV model, where the system undergoes a tricritical Ising transition by tuning just one parameter. In this work, we generalize this model to a ladder with inter-chain Majorana couplings. From a mean field analysis, we argue that the tricritical Ising transition will also occur with inter-chain couplings that allow the system to be gapless in the non-interacting case. More crucially, based on analysis of the interacting chain model and the non-interacting ladder model, we expect the tricritical Ising modes to appear on the edges, a feature that might persist when going to 2d. We carry out extensive DMRG calculations to verify the theory in the ladder model. Finally, we discuss possible numerical probes of a 2d model.Science, Faculty of
Physics and Astronomy, Department of
Graduate
3
Pugh, Mathew. "Ising model and beyond." Thesis, Cardiff University, 2008. http://orca.cf.ac.uk/54791/.
Анотація:
We study the SU(3) AVE graphs, which appear in the classification of modular in variant partition functions from numerous viewpoints, including determination of their Boltzmann weights, representations of Hecke algebras, a new notion of A2 planar algebras and their modules, various Hilbert series of dimensions and spectral measures, and the K-theory of associated Cuntz-Krieger algebras. We compute the K-theory of the of the Cuntz-Krieger algebras associated to the SU(3) AVE graphs. We compute the numerical values of the Ocneanu cells, and consequently representations of the Hecke algebra, for the AVE graphs. Some such representations have appeared in the literature and we compare our results. We use these cells to define an SU(3) analogue of the Goodman-de la Harpe-Jones construction of a subfactor, where we embed the j42-Temperley-Lieb algebra in an AF path-algebra of the SU(3) AVE graphs. Using this construction, we realize all SU(3) modular invariants by subfactors previously announced by Ocneanu. We give a diagrammatic representation of the i42-Temperley-Lieb algebra, and show that it is isomorphic to Wenzl's representation of a Hecke algebra. Generalizing Jones's notion of a planar algebra, we construct an 42-planar algebra which captures the structure contained in the SU(3) AVE subfactors. We show that the subfactor for an AVE graph with a flat connection has a description as a flat >12-planar algebra. We introduce the notion of modules over an 42-planar algebra, and describe certain irreducible Hilbert A2- Temperley-Lieb-modules. A partial decomposition of the ,42-planar algebras for the AVE graphs is achieved. We compare various Hilbert series of dimensions associated to ADE models for SU(2), and the Hilbert series of certain Calabi-Yau algebras of dimension 3. We also consider spectral measures for the ADE graphs and generalize to SU(3), and in particular obtain spectral measures for the infinite SU(3) graphs.
4
Marsolais, Annette M. "The Equivalence Between the Kitaev, the Transverse Quantum Ising Model and the Classical Ising Model." University of Akron / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=akron1619792923386843.
5
Silva, Romero Tavares da. "ALEATORIEDADE EM MODELOS DE ISING." Universidade de São Paulo, 1993. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-22052012-133450/.
Анотація:
Na primeira parte deste trabalho propomos uma aproximacão de campo médio dinâmico para analisar modelos de Ising com elementos e aleatoriedade definidos por distribuicões de probabilidades discretas. Analisamos o modelo com campo aleatório (S = 1/2), com interações aleatórias (S = 1/2), com diluição de sítios (S = 1/2) e com anisotropia aleatória (S = 1), obtendo os respectivos diagramas de fases. Na segunda parte analisamos modelos de vidros de spin (S= 3/2) com anisotropia de campo cristalino. Estudamos o modelo de van Hemmen, e o modelo clássico à la Sherrington e Kirkpatrick dentro do esquema de réplicas simétricas, obtendo os diagramas de fases correspondentes.In the first part of this work we propose a dynamical mean field approximation to analyse Ising models with elements of randomnss, defined by discret probability functions. We have analysed the random field model (S = 1/2); the random bond model (S = 1/2); the site diluted model (S = 3/2) and the random crystal field model (S = 1), obtaining the respective phase diagrams. In the second part we have analysed spinglass models (S = 3/2) in the presence of a crystal field. We have studied the van Hemmen and the classic spin glass model à la Sherrington and Kirkpatrick, using replica symmetric scheme, to obtain the corresponding phase diagrams.
6
Ridderstolpe, Ludwig. "Exact Solutions of the Ising Model." Thesis, Uppsala universitet, Teoretisk astrofysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-329081.
Анотація:
This report presents the general Ising model and its basic assumptions. This study aims to, from diagonalization of the Transfer Matrix, obtain the Helmholtz free energy and the exclusion of a phase transition for the one-dimensional Ising model under an external magnetic field. Furthermore from establishing the commutation relations of the Transfer matrices and using the Kramers-Wannier duality one finds the free energy and the presence of a phase transition for the square-lattice Ising model.
7
Smith, Thomas H. R. "Driven interfaces in the Ising model." Thesis, University of Bristol, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535182.
8
Gray, Sean. "Bootstrapping the Three-dimensional Ising Model." Thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-322146.
Анотація:
This thesis begins with the fundamentals of conformal field theory in three dimensions. The general properties of the conformal bootstrap are then reviewed. The three-dimensional Ising model is presented from the perspective of the renormalization group, after which the conformal field theory aspect at the critical point is discussed. Finally, the bootstrap programme is applied to the three-dimensional Ising model using numerical techniques, and the results analysed.
9
Tamashiro, Mário Noboru. "Modelos de Ising com Competição." Universidade de São Paulo, 1996. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-28022014-163442/.
Анотація:
Neste trabalho consideramos três modelos de Ising com competição: que é gerada por acoplamentos dinâmicos de caráter antagônicos, pela própria geometria da rede subjacente ou através de interações de periodicidades uniaxiais competitivas e elementos de desordem. O primeiro modelo, no qual as técnicas de mecânica estatística de equilíbrio não se aplicam, consiste numa rede neural atratora completamente conectada com acoplamentos assimétricos armazenando p = 2 padrões, cuja evolução temporal pode ser descrita (no caso de atualização síncrona) por um mapeamento dissipativo bidimensional. O segundo modelo se refere ao problema clássico do antiferromagneto de Ising na rede triangular na presença de um campo magnético uniforme, investigado através de diversas aproximações - em particular, através de uma aproximação de Bethe-Peierls considerando três sub-redes interpenetrantes equivalentes. O terceiro modelo, introduzido para investigar o efeito de uma desordem congelada em um sistema magnético modulado, é definido pelo modelo ANNNI em um campo aleatório. Inicialmente consideramos um análogo deste modelo na árvore de Cayley, no limite de coordenação infinita, que pode ser formulado em termos de um mapeamento dissipativo bidimensional. A seguir, consideramos uma versão de campo médio em uma rede cúbica simples. que permite uma análise das superfícies de transição de primeira ordem e das linhas tricriticas.In this work we consider three Ising models with competition: which is generated by dynamical couplings of antagonistic character, by the geometry of the underlying lattice, or by interactions of competitive uniaxial periodicities and disorder elements. The first model, for which equilibrium statistical mechanics techniques do not apply, consists in a fully connected attractor neural network storing p = 2 patterns, whose temporal evolution can be described (in the case of synchronous updating) by a two-dimensional dissipative mapping. The second model refers to the classic problem of the Ising antiferromagnet on the triangular lattice in the presence of a uniform magnetic field, which is investigated by various approximations - in particular, by a Bethe-Peierls approximation considering three interpenetrating equivalent sublattices. The third model, introduced to investigate the effects of quenched disorder in a modulated magnetic system, is defined by the ANNNI model in a random field. Initially we consider an analogous of this model on a Cayley tree, in the infinite-coordination limit, which can be formulated in terms of a two-dimensional dissipative mapping. Next, we consider a mean-field version on a simple cubic lattice, which allows for an analysis of the first-order transition surfaces and tricritical lines.
10
Hystad, Grethe. "Periodic Ising Correlations." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/196130.
Анотація:
We consider the finite two-dimensional Ising model on a lattice with periodic boundaryconditions. Kaufman determined the spectrum of the transfer matrix on the finite,periodic lattice, and her derivation was a simplification of Onsager's famous result onsolving the two-dimensional Ising model. We derive and rework Kaufman's resultsby applying representation theory, which give us a more direct approach to computethe spectrum of the transfer matrix. We determine formulas for the spin correlationfunction that depend on the matrix elements of the induced rotation associated withthe spin operator. The representation of the spin matrix elements is obtained byconsidering the spin operator as an intertwining map. We wrap the lattice aroundthe cylinder taking the semi-infinite volume limit. We control the scaling limit of themulti-spin Ising correlations on the cylinder as the temperature approaches the criticaltemperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrixelements on the finite, periodic lattice. Finally, we compute the matrix representationof the spin operator for temperatures below the critical temperature in the infinite-volume limit in the pure state defined by plus boundary conditions.
11
Sakellariou, Jason. "Inverse inference in the asymmetric Ising model." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00869738.
Анотація:
Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.
12
Brown, A. S. "Critical phenomena in the Random Ising Model." Thesis, University of Edinburgh, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370906.
13
Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models : Stochastic geometry of the quantum Ising model and the space-time Potts model." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11267.
Анотація:
HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in 
. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in and in ‘star-like’ geometries.HTML clipboard Statistisk fysik syftar till att förklara ett materials makroskopiska egenskaper i termer av dess mikroskopiska struktur. En särskilt intressant egenskap är är fenomenet fasövergång, det vill säga en plötslig förändring i de makroskopiska egenskaperna när externa förutsättningar varieras. Två modeller är särskilt intressanta för en matematiker, nämligen Ising-modellen av en magnet och perkolationsmodellen av ett poröst material. Dessa två modeller sammanförs av den så-kallade fk-modellen, en slumpgrafsmodell som först studerades av Fortuin och Kasteleyn på 1970-talet. fk-modellen har sedermera visat sig vara extremt användbar för att bevisa viktiga resultat om Ising-modellen och liknande modeller. I den här avhandlingen studeras den motsvarande grafiska strukturen hos två näraliggande modeller. Den första av dessa är den kvantteoretiska Isingmodellen med transverst fält, vilken är en utveckling av den klassiska Isingmodellen och först studerades av Lieb, Schultz och Mattis på 1960-talet. Den andra modellen är rumtid-perkolation, som är nära besläktad med kontaktmodellen av infektionsspridning. I Kapitel 2 definieras rumtid-fk-modellen, och flera probabilistiska verktyg utforskas för att studera dess grundläggande egenskaper. Vi möter rumtid-Potts-modellen, som uppenbarar sig som en naturlig generalisering av den kvantteoretiska Ising-modellen. De viktigaste egenskaperna hos fasövergången i dessa modeller behandlas i detta kapitel, exempelvis det faktum att det i fk-modellen finns högst en obegränsad komponent, samt den undre gräns för det kritiska värdet som detta innebär. I Kapitel 3 utvecklas en alternativ grafisk framställning av den kvantteoretiska Ising-modellen, den så-kallade slumpparitetsframställningen. Denna är baserad på slumpflödesframställningen av den klassiska Ising-modellen, och är ett verktyg som låter oss studera fasövergången och gränsbeteendet mycket närmare. Huvudsyftet med detta kapitel är att bevisa att fasövergången är skarp—en central egenskap—samt att fastslå olikheter för vissa kritiska exponenter. Metoden består i att använda slumpparitetsframställningen för att härleda vissa differentialolikheter, vilka sedan kan integreras för att lägga fast att gränsen är skarp. I Kapitel 4 utforskas några konsekvenser, samt möjliga vidareutvecklingar, av resultaten i de tidigare kapitlen. Exempelvis bestäms det kritiska värdet hos den kvantteoretiska Ising-modellen på
, samt i ‘stjärnliknankde’ geometrier.QC 20100705
14
Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models stochastic geometry of the quantum Ising model and the space-time Potts model /." Stockholm : Skolan för teknikvetenskap, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11267.
15
Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models : stochastic geometry of the quantum Ising model and the space-time Potts model." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/224774.
Анотація:
Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970's. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second model is the space-time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate 'space-time' random-cluster model and explore a range of useful probabilistic techniques for studying it. The space-time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in Z. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model - a central issue in the theory - and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which give the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in Z and in 'star-like' geometries.
16
Feng, Shuangtong. "Efficient Parallelization of 2D Ising Spin Systems." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/36263.
Анотація:
The problem of efficient parallelization of 2D Ising spin systems requires realistic algorithmic design and implementation based on an understanding of issues from computer science and statistical physics. In this work, we not only consider fundamental parallel computing issues but also ensure that the major constraints and criteria of 2D Ising spin systems are incorporated into our study. This realism in both parallel computation and statistical physics has rarely been reflected in previous research for this problem.
In this thesis,we designed and implemented a variety of parallel algorithms for both sweep spin selection and random spin selection. We analyzed our parallel algorithms on a portable and general parallel machine model, namely the LogP model. We were able to obtain rigorous theoretical run-times on LogP for all the parallel algorithms. Moreover, a guiding equation was derived for choosing data layouts (blocked vs. stripped) for sweep spin selection. In regards to random spin selection, we were able to develop parallel algorithms with efficient communication schemes. We analyzed randomness of our schemes using statistical methods and provided comparisons between the different schemes. Furthermore, algorithms were implemented and performance data gathered and analyzed in order to determine further design issues and validate theoretical analysis.
Master of Science
17
Hernández, José Javier Cerda. "Ising and Potts model coupled to Lorentzian triangulations." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-18032015-170430/.
Анотація:
The main objective of the present thesis is to investigate: What are the properties of the Ising and Potts model coupled to a CDT emsemble? For that objective, we used two methods: (1) transfer matrix formalism and Krein-Rutman theory. (2) FK representation of the q -state Potts model on CDTs and dual CDTs. Transfer matrix formalism permite us to obtain spectral properties of the transfer matrix using the Krein-Rutman theorem [KR48] on operators preserving the cone of positive func- tions. This yields results on convergence and asymptotic properties of the partition function and the Gibbs measure and allows us to determine regions in the parameter quarter-plane where the free energy converges. Second methods permite us to determine a region in the quadrant of parameters , > 0 where the critical curve for the classical model can be located. We also provide lower and upper bounds for the innite-volume free energy. Finally, using arguments of duality on graph theory and hight-T expansion we study the Potts model coupled to CDTs. This approach permite us to improve the results obtained for Ising model and obtain lower and upper bounds for the critical curve and free energy. Moreover, we obtain an approximation of the maximal eigenvalue of the transfer matrix at lower temperature.O objetivo principal da presente tese é pesquisar : Quais são as propriedades do modelo de Ising e Potts acoplado ao emsemble de CDT? Para estudar o modelo usamos dois métodos: (1) Matriz de transferência e Teorema de Krein-Rutman. (2) Representação FK para o modelo de Potts sobre CDT e dual de CDT. Matriz de transferência permite obter propriedades espectrais da Matriz de transferência utilizando o Teorema de Krein-Rutman [KR48] sobre operadores que conservam o cone de funções positivas. Também obtemos propriedades asintóticas da função de partição e das medidas de Gibbs. Esses propriedades permitem obter uma região onde a energia livre converge. O segundo método permite obter uma região onde a curva crítica do modelo pode estar localizada. Além disso, também obtemos uma cota superior e inferior para a energia livre a volume infinito. Finalmente, utilizando argumentos de dualidade em grafos e expansão em alta temperatura estudamos o modelo de Potts acoplado as triangulações causais. Essa abordagem permite generalizar o modelo, melhorar os resultados obtidos para o modelo de Ising e obter novas cotas, superior e inferior, para a energia livre e para a curva crítica. Além disso, obtemos uma aproximação do autovalor maximal do operador de transferência a baixa temperatura.
18
Aronsen, Kristoffer. "Quantum Criticality in the Transverse Field Random Ising Model." Thesis, KTH, Fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-257771.
19
Cochran, Christopher S. "Even-number spin correlations on two-dimensional Ising lattice structures." Virtual Press, 2002. http://liblink.bsu.edu/uhtbin/catkey/1237760.
Анотація:
Many physical systems can be represented by a regular arrangement of molecules in a lattice structure. Knowing how neighboring molecules in the lattice interact with one another can give great insight into a material's macroscopic behavior. A very popular and effective means of investigating these microscopic interactions is the Ising Model. This model, suggested first by Wilhelm Lenz in 1920 and later expanded by Ernst Ising in 1925, is based on the assumptions that each molecule in a lattice structure can be represented by its spin value (+l or -1) and that only nearest neighbors contribute to the total interaction energy. The Ising Model, which was initially used in the study of ferromagnetic systems, can now be used to study a variety of physical systems. Some of these include antiferromagnetic crystals, binary alloys, DNA, and lattice gasses.Department of Physics and Astronomy
20
Friedenauer, Axel. "Simulation of the Quantum Ising Model in an Ion Trap." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-115958.
21
Valani, Yogendra P. "On the partition function for the three-dimensional Ising model." Thesis, City University London, 2011. http://openaccess.city.ac.uk/11667/.
Анотація:
Our aim is to investigate the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state Potts model partition functions on two- and three-dimensional lattices are also computed and analysed. Our results are analysed as distributions of zeros of the partition function in the complex-temperature plane. We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model.
22
Goncalves, Jose Ramos. "A theoretical study of the frustrated two-dimensional Ising model." Thesis, University of Reading, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360789.
23
Mossa, Alessandro. "Analytic Properties of the Free Energy: the Tricritical Ising Model." Doctoral thesis, SISSA, 2004. http://hdl.handle.net/20.500.11767/3983.
24
Dinóla, Isabel Cristina Souza. "Super Antiferromagneto de Ising com campo uniforme." Universidade Federal do Amazonas, 2009. http://tede.ufam.edu.br/handle/tede/4543.
Анотація:
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The phase diagram of the two-dimensional super-antiferromagnetic (SAF) Ising model in the presence of a magnetic field is investigated within the framework of a real-space renormalization-group approximation. We consider nearest neighbor ferromagnetic interactions along the x(y) direction and antiferromagnetic interactions in the y(x) direction. The system presents a ordered phase at low temperatures and zero fields. The presence of a magnetic field induces a competition between the energy interactions of the SAF Hamiltonian. The resulting behavior has been a matter of controversy in the last years. We depicted the main results in the magnetic field versus temperature phase diagram. A second-order transition line separates a super-antiferromagnetic phase from a field induced ferromagnetic phase. Our study reveals that the magnetic field induces a phase transition at a single temperature value, thus, we did not find any evidence of reentrant behavior as claimed by some authors.
Utilizamos uma técnica de grupo de renormalização no espaço real para estudar o sistema super antiferromagneto (SAF) de Ising bidimensional sob a influência de um campo magnético externo. Neste modelo as interações de primeiros vizinhos na direção x são ferromagnéticas e na direção y são antiferromagnéticas. Este sistema apresenta uma fase ordenada, para baixas temperaturas e campos nulos, com uma estrutura de linhas ferromagnéticas e colunas antiferromagnéticas. A aplicação do campo magnético induz uma competição entre as energias de interação do modelo e o comportamento resultante desta competição tem sido objeto de estudo e gerado algumas controvérsias nos últimos anos. Na presença do campo magnético observa-se, além da fase SAF, a fase ferromagnética induzida pelo campo (FIC). Apresentamos neste trabalho o diagrama de fases completo do sistema SAF no plano temperatura versus campo magnético. O diagrama de fases obtido mostra uma linha de transição de segunda ordem separando a fase SAF da fase FIC. Nossos resultados contrariam resultados anteriores que preveêm um comportamento reentrante no diagrama de fases do sistema SAF.
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Hazbun, Nagib Miguel. "Algumas aplicações de invariância conforme no estudo de fenômenos críticos." Universidade de São Paulo, 1990. http://www.teses.usp.br/teses/disponiveis/54/54131/tde-04042014-093330/.
Анотація:
Neste trabalho apresentamos alguns resultados da invariância conforme e da teoria de escala para sistemas finitos. Estudamos, usando tais técnicas, dois modelos estatísticos (modelos 1 e 2). Para cada modelo obtivemos a anomalia conforme e as dimensões dos operadores energia e magnetização bem como seus respectivos descendentesIn this work we show some results of conformal invariance theory and finite-size scaling. We study by using these theories two statistical mechanics models (models 1 and 2). To each model we obtained the conformal anomaly, the dimensions of energy and magnetization operators as well their respective descendents
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Goff, Leonard Thomas. "Surface codes, the 2D classical Ising model, and non-interacting fermions." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/36374.
Анотація:
In this thesis, we consider the task of simulating measurement-based quantum computation (MBQC) on surface code states: the generalization of Kitaev's toric code to graphs embedded on a surface of higher genus. We define a family of higher genus graphs and a simple ordering of single qubit measurements, and find that simulating MBQC on any of the associated surface code states is equivalent to evaluating the inner-product between a product state and a surface code state on another graph. We further find that such an inner-product can always be written as a sum of one or more 2D classical Ising model partition functions, with appropriate couplings. For certain higher genus square lattices, we develop a means to evaluate this partition function in a number of steps that scales polynomially in the number of qubits, but exponentially in the genus of the embedded graph. The method makes use of the transfer matrix formalism for the Ising partition function, and a subsequent mapping to fermion operators. We synthesize these results to relate the simulation of MBQC on certain surface code states to a system of fermions interacting with the encoded qubits of the surface code. We identify a family of states in the code space of the surface code on our higher genus graphs for which MBQC can be simulated efficiently in all parameters, including the genus of the embedded graph. Finally, we identify two connections between the complexity of this task and entanglement.
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CARAGLIO, MICHELE. "Mechanical unfolding and confinement of proteinsinvestigated through an Ising-like model." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2496126.
Анотація:
Un semplice modello alla Ising viene utilizzato per studiare le proprietà di equilibrio e la cinetica di biomolecole alle quali vengono applicate delle forze, tipicamente alle estremità, o tra particolari coppie di aminoacidi, o ancora confinandole tra una coppia di pareti rigide.
Nel caso della fibronectina, più precisamente del suo decimo domino di tipo III, FnIII10, è stato studiato l'unfolding meccanico secondo i protocolli a forza costante e velocità costante. È stato possibile determinare i pathways di unfolding, confermando risultati precedenti nel caso di forze e velocità grandi, ed esplorando, grazie alla semplicità del modello, valori di forza e velocità più bassi, rilevanti per il comportamento in vivo della molecola. In questo caso è stato messo in evidenza un possibile fenomeno di fluttuazione tra 2 stati intermedi.
Nel caso della proteina fluorescente verde (GFP), dopo aver confermato risultati precedenti per il caso in cui la molecola viene tirata dalle estremità, il lavoro si è concentrato sulla dipendenza dei parametri cinetici (forze e lunghezze di unfolding) dalla direzione, ovvero dalla coppia di aminoacidi ai quali la forza viene applicata. Questo lavoro ha dato risultati qualitativamente in accordo con gli esperimenti e, laddove disponibili, con simulazioni di modelli più dettagliati. Ha inoltre permesso di formulare una proposta per un sensore di forza basato su una poliproteina costituita da diversi moduli di GFP opportunamente connessi tra loro.
Infine, il modello è stato esteso al caso del folding in uno spazio confinato, precisamente tra 2 pareti rigide inerti, mostrando che, nonostante la sua semplicità, il modello è in grado di descrivere i fenomeni di innalzamento della temperatura di denaturazione e del folding rate osservati sperimentalmente, e le rispettive leggi a potenza.
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Hernandez, Hernandez Fabio 1990. "Estados de impureza no modelo de Ising quântico." [s.n.], 2016. http://repositorio.unicamp.br/jspui/handle/REPOSIP/322412.
Анотація:
Orientador: Guillermo Gerardo Cabrera OyarzúnDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: A descrição da dinâmica quântica de sistemas de muitos corpos é um ingrediente chave para computação e simulações quânticas. No presente projeto, estudamos a dinâmica de cadeias de spin na presença de impurezas ou defeitos. O sistema de Ising quantico (Ising com campo transverso) com uma impureza foi solucionado de forma exata. Este sistema de spins pode ser simulado de forma analítica por partículas quânticas (transformação de Jordan-Wigner). Caracterizamos o espectro, as autofunções e a evolução temporal da magnetização para estados iniciais particulares, focando no papel desempenhado pelos estados de impureza. Finalmente observamos oscilações remanescentes na magnetização, após a relaxação do sistema, para alguns valores dos parâmetros da impureza nos quais existem dois estados ligados no espectro de energias
Abstract: The description of dynamics of quantum many-body systems is a key ingredient to perform quantum computation and/or simulations of quantum behavior. In the present proposal, we study the time evolution of quantum spin chains with impurities at one of the boundaries, in order to understand the role of defects in relaxation properties. The quantum (transverse) Ising model with an impurity has been solved in exact form, using the Jordan-Wigner transformation, where spins are mapped onto spinless fermions, thus simulating analytically a spin system with particles. We completely characterize the spectrum, with the presence of bound states depending on values of the impurity parameters. We calculate the local magnetization and observe its relaxation for particular non-homogeneous initial states. Surprisingly, remanent Rabi oscillations are observed at asymptotically long times, when the spectrum displays two bound states
Mestrado
Física
Mestre em Física
1247646/2013
CAPES
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Zhao, Yang, and Min Zhang. "The Ising Model on a Heavy Gravity Portfolio Applied to Default Contagion." Thesis, Högskolan i Halmstad, Tillämpad matematik och fysik (MPE-lab), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16459.
Анотація:
In this paper we introduce a model of default contagion in the financail market. The structure of the companies are represented by a Heavy Gravity Portfolio, where we assume there are N sectors in the market and in each sector i, there is one big trader and ni supply companies.The supply companies in each sector are directly inuenced by the bigtrader and the big traders are also pairwise interacting with each other.This development of the Ising model is called Heavy gravity portfolioand according to this, the relation between expectation and correlationof the default of companies are derived by means of simulations utilisingthe Gibbs sampler. Finally methods for maximum likelihood estimationand for a likelihood ratio test of the interaction parameter in the modelare derived.
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Jäderlund, Thom. "A scaling approach to critical exponent calculations for the 2D Ising model." Thesis, KTH, Fysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-274382.
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Navarrete, Manuel Alejandro Gonzalez. "Modelo de Ising ferromagnético com campo externo periódico." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-28082015-000711/.
Анотація:
Estudamos o diagrama de fases para uma classe de modelos de Ising ferromagnéticos em $ \\mathbb^2 $, com campo magnético externo periódico. O campo externo assume dois valores: $ h $ e $ -h $, onde $ h> 0 $. Os sítios associados a valores positivos e negativos do campo externo, formam uma configuração em forma de tabuleiro de xadrez (nós chamamos de {\\it cell-board configuration}), com células retangulares de tamanho $ L_1 \\times L_2 $ sítios, de tal forma que o valor total do campo externo é zero. Como principal resultado, mostramos a presença de uma transição de fase de primeira ordem. A transição de fase existe para $ h <\\frac + \\frac $, onde $ J $ é uma constante de interação. A prova é construida usando o método de {\\it reflection positivity (RP)}. Aplicamos uma desigualdade que é normalmente referida como a estimativa de {\\it chessboard}. Além disso, incluímos uma região de unicidade da medida de Gibbs em $h>4J$, isto usando um critério baseado nas ideias de percolação em desacordo.We study the low-temperature phase diagram for a ferromagnetic Ising model on $\\mathbb^2$, with a periodical external magnetic field. The external field takes two values: $h$ and $-h$, where $h>0$. The sites associated with positive and negative values of external field form a cell-board configuration with rectangular cells of sides $L_1\\times L_2$ sites, such that the total value of the external field is zero. As a main result, we show the presence of a first-order phase transition. The phase transition holds if $h<\\frac+ \\frac$, where $J$ is an interaction constant. We use the reflection positivity (RP) method. We apply a key inequality which is usually referred to as the chessboard estimate. Furthermore, we prove uniqueness for Gibbs measure in $h>4J$, using a uniqueness condition obtained in terms of disagreement percolation.
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CAMPAJOLA, Carlo. "Modelling financial lead-lag interactions with Kinetic Ising Models." Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/90680.
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Davison, Lexie. "Glassy behaviour in simple systems." Thesis, University of Oxford, 2001. http://ora.ox.ac.uk/objects/uuid:10c594d7-1fa5-45f5-bba4-0fefb837aadf.
Анотація:
In this thesis we study several different models which display glassy behaviour. Firstly, we investigate a simple, purely topological, cellular model for which the Hamiltonian is non-interacting but the dynamics are constrained. We find a non-thermodynamic transition to a glassy phase in which the energy fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. This model involves activated processes and displays two-step relaxation in both the energy and the correlation functions; the latter also exhibit signs of aging. The relaxation time can be well-fitted at all temperatures by an offset Arrhenius law. Some predictions of Mode-coupling Theory are tested with some agreement found, but no convincing evidence that this description is the most fitting. By defining a suitable response function, we find that the equilibrium Fluctuation-Dissipation Theorem (FDT) is upheld for all but very short waiting-times, despite the fact that the system is not in equilibrium. This topological model is simplified to a hexagonally-based spin model, which also displays glassy behaviour, involves activated processes and exhibits two-step relaxation. This is a consequence of reaction-diffusion processes on two different time-scales, one temperature-independent and the other an exponential function of inverse temperature. We study two versions of this model, one with a single absorbing ground state, and the other with a highly degenerate ground state. These display qualitatively similar but quantitatively distinct macroscopic behaviour, and related but different microscopic behaviour. We extend this work to a square lattice, and find that the geometry of the lattice has a considerable impact on the behaviour, and to three dimensions, which provides support for the reaction-diffusion classification of the early behaviour. We find observable-dependent FDT plots; the observable can be chosen such that FDT is upheld for a region whilst the system is out of equilibrium — this observation is supported by some preliminary results for one-dimensional kinetically-constrained Ising chains.
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Nowotny, Thomas. "Phase transitions and multifractal properties of random field Ising models." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37023.
Анотація:
In dieser Arbeit werden Zufallsfeld-Ising-Modelle mit einem eingefrorenen dichotomen symmetrischen Zufallsfeld für den eindimensionalen Fall und das Bethe-Gitter untersucht. Dabei wird die kanonische Zustandssumme zu der eines einzelnen Spins in einem effektiven Feld umformuliert. Im ersten Teil der Arbeit werden das mulktifraktale Spektrum dieses effektiven Feldes untersucht, Übergänge im Spektrum erklärt und Ungleichungen zwischen lokalen und globalen Dimensionsbegriffen bewiesen, die eine weitgehend vollständige Charakterisierung des multifraktalen Spektrums durch eine Reihe von Schranken erlauben. Ein weiterer Teil der Arbeit beschäftigt sich mit einer ähnlichen Charakterisierung des Maßes der lokalen Magnetisierung, das aus dem Maß des effektiven Feldes durch Faltung hervorgeht. In diesem Zusammenhang wird die Faltung von Multifraktalen in einem allgemeineren Rahmen behandelt und Zusammenhänge zwischen den multifraktalen Eigenschaften der Faltung und denen der gefalteten Maße bewiesen. Im dritten Teil der Dissertation wird der Phasenübergang von Ferro- zu Paramagnetismus im Modell auf dem Bethe Gitter untersucht. Neben verbesserten exakten Schranken für die Eindeutigkeit des paramagnetischen Zustands werden im wesentlichen drei Kriterien für die tatsächliche Lage des Übergangs angegeben und numerisch ausgewertet. Die multifraktalen Eigenschaften des effektiven Felds im Modell auf dem Bethe-Gitter schließlich erweisen sich als trivial, da die interessanten Dimensionen nicht existierenIn this work random field Ising models with quenched dichotomous symmetric random field are considered for the one-dimensional case and on the Bethe lattice. To this end the canonical partition function is reformulated to the partition function of one spin in an effective field. In the first part of the work the multifractal spectrum of this effective field is investigated, transitions in the spectrum are explained and inequalities between local and global generalized fractal dimensions are proven which allow to characterize the multifractal spectrum bei various bounds. A further part of the work is dedicated to the characterization of the measure of the local magnetization which is obtained by convolution of the measure of the effective field with itself. In this context the convolution of multifractals is investigated in a more general setup and relations between the multifractal properties of the convolution and the multifractal properties of the convoluted measures are proven. The phase transition from ferro- to paramagnetismus for the model on the Bethe lattice is investigated in the third part of the thesis. Apart from improved exact bounds for the uniqueness of the paramagnetic state essentially three criteria for the transition are developped and numerically evaluated to determine the transition line. The multifractal properties of the effective field for the model on the Bethe lattice finally turn out to be trivial because the interesting dimensions do not exist
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Kong, Chi-Wah. "Monte-Carlo simulation on a 2-D random point pattern : ising model and its application to econophysics /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202002%20KONG.
Анотація:
Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002.Includes bibliographical references (leaves 81-82). Also available in electronic version. Access restricted to campus users.
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Bohorquez, Oscar Alberto Barbosa. "Irreversibilidade por competição para um modelo de Glauber-Ising a partir da produção de entropia." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14032013-221122/.
Анотація:
Trata-se um sistema irreversível e fora do equilíbrio adotando uma dinâmica estocástica, a partir de uma abordagem que visa a compreensão dos efeitos macroscópicos como uma consequência das características microscópicas do sistema. O estudo enfoca-se sobre as transições de fase cinéticas que têm lugar pela adoção de um modelo de rede, no intuito de descrever os estados estacionários por meio da produção de entropia, que caracteriza o comportamento do sistema elucidando as suas condições de reversibilidade. Dessa forma considera-se um modelo de Ising cinético com simetria \\textit{up-down} e sob a influência de duas dinâmicas de Glauber em competição. Nesse sentido considera-se uma rede quadrada constituída por duas subredes atreladas, as quais submetem-se ao contato de reservatórios térmicos a diferentes temperaturas. O estudo é feito mediante a adoção de uma abordagem analítica assumindo uma aproximação de campo médio, e, do mesmo modo, com base em resultados de caráter numérico obtidos com simulações de Monte Carlo. Os resultados mostram uma transição de fase de segunda ordem no regime de não equilíbrio, a qual é refletida numa divergência logarítmica na derivada da produção de entropia.An irreversible and out of equilibrium system is analyzed by means of a stochastic dynamics based on an approach that aims to understand the macroscopic effects as a consequence of the microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model, intended to describe the stationary states by the entropy production, which characterize the system behavior, clarifying the reversibility conditions. Thus a kinetic Ising model with up-down symmetry and under the influence of two competing Glauber dynamics is analized. In this sense one considers a square lattice formed by two sublattices interconnected, which are in contact with two heat baths at different temperatures. The study is made by means of the analytical approach of a mean-field approximation and Monte Carlo simulations. The results show a phase transition of the second order in the steady state regime, which is evidenced by a logarithmic divergence of the entropy production derivative.
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Velasco-Cruz, Ciro. "Spatially Correlated Model Selection (SCOMS)." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27791.
Анотація:
In this dissertation, a variable selection method for spatial data is developed. It is assumed that the spatial process is non-stationary as a whole but is piece-wise stationary. The pieces where the spatial process is stationary are called regions. The variable selection approach accounts for two sources of correlation: (1) the spatial correlation of the data within the regions, and (2) the correlation of adjacent regions.
The variable selection is carried out by including indicator variables that characterize the significance of the regression coefficients. The Ising distribution as prior for the vector of indicator variables, models the dependence of adjacent regions.
We present a case study on brook trout data where the response of interest is the presence/absence of the fish at sites in the eastern United States. We find that the method outperforms the case of the probit regression where the spatial field is assumed stationary and isotropic. Additionally, the method outperformed the case where multiple regions are assumed independent of their neighbors.Ph. D.
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Pachêco, Vanusa Bezerra. "Efeitos de superfície e frustração nas propriedades críticas do modelo de Ising." Universidade Federal do Amazonas, 2006. http://tede.ufam.edu.br/handle/tede/3465.
Анотація:
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Previous issue date: 2006-12-01Fundação de Amparo à Pesquisa do Estado do Amazonas
Neste trabalho investigamos o diagrama de fase do modelo de Ising de spin ½ aleatoriamente decorado nos planos de um filme fino de tamanho L. As interações nos planos simula a interação cobre-cobre (Cu-Cu) numa rede cúbica simples antiferromagnética, onde entre os vértices da rede coloca-se um spin decorador aleatoriamente distribuído, que simula o íon de oxigênio no plano de cobre-oxigênio (CuO2) de valor ½ e interagindo ferromagneticamente com os íons de cobre, provocando assim o fenômeno de frustração. Para este estudo, utilizamos a técnica do operador diferencial em aglomerado com um íon em conjunto com a aproximação do campo efetivo. Através dos diagramas de fase (formúla), onde (formúla) , que representa a relação das energias de interação ferromagnética da superfície com o bulk é possível notar um ponto multicrítico (formúla) que corresponde ao caso em que tanto a superfície quanto o bulk estão ordenados a um dado valor de concentração e valores para os parâmetros de frustrações (formúla) (parâmetro de frustração da superfície) e (formúla) (parâmetro de frustração do bulk). Para valores Δ < Δc, o sistema apresenta-se com bulk ordenado e a superfície desordenada, isto significa que a temperatura crítica do bulk ( b ) c T é maior que a temperatura crítica da superfície ( s ) c T , no entanto para Δ >Δc a superfície está ordenada e o bulk desordenado, isto é, . E para (formúla) verificamos que para determinados valores de concentração encontramos para qualquer valor de Δ os mesmos valores de temperaturas críticas.
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Calderon, Filho Cesar José 1987. "Estudo teórico de sistemas de elétrons fortemente correlacionados = aplicação aos multiferróicos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277846.
Анотація:
Orientadores: Gaston Eduardo Barberis, Pascoal José Giglio PagliusoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: Na física da materia condensada, o estudo de sistemas de eletrons fortemente correlacionados é, com certeza, um dos problemas mais interessantes tanto do ponto de vista experimental como teórico, e são estes materiais que tem sido utilizados recentemente em aplicações tecnológicas. Destes compostos, os multiferroicos apresentam um conjunto de propriedades físicas muito rico. Estes materiais apresentam pelo menos duas das seguintes correlações de longo alcance: (anti)ferromagnetismo, ferroelasticidade e ferroeletricidade. Porém, as transições não precisam ser necessariamente correlacionadas, mas quando são, estas ocorrem simultaneamente, e o efeito magnetoelétrico pode ser induzido por campo. Neste trabalho, foram desenvolvidos cálculos numéricos que simulam o acoplamento magnetoelétrico presente nos multiferróicos minimizando a energia através da técnica de Monte Carlo. Foram desenvolvidos dois modelos muito simples. O primeiro modelo acopla uma rede de Ising 2D com spin 1/2 com uma rede de dipolos elétricos tambem 2D; este acoplamento e tal que a mudança de direção de um dado spin reorienta uma dada componente perpendicular do dipolo elétrico vizinho a este mesmo spin. Assim, para este primeiro modelo, as transições de fase das redes elétrica e magnetica ocorrem na mesma temperatura, sendo o hamiltoniano dependente de três parâmetros. Para o segundo modelo, foram utilizadas novamente duas redes, uma rede de Ising 2D com spin 1/2, e uma rede elétrica que se comporta da mesma maneira que uma rede de Ising 2D. Neste caso, o acoplamento entre o spin e o dipolo eletrico ocorre através de um sistema de dois níveis, gerando a possibilidade de temperaturas de transição independentes para as duas redes. Este segundo modelo tambem depende de três parâmetros
Abstract: In condensed matter physics, the study of strongly correlated electron systems is certainly one of the most interesting problems both from the experimental and the theoretical points of view, also these materials recently being used in technological applications. Among these compounds, the multiferroics show a very rich set of physical properties. These materials have at least two of the following long-range correlations: (anti)ferromagnetism, ferroelasticity and ferroelectricity. However, the transitions need not necessarily to be correlated, but when it happens, they occur simultaneously, and the magnetoelectric effect can be induced by field. In this work, numerical calculations have been developed to simulate the magnetoelectric coupling present in the multiferroics minimizing the energy through Monte Carlo technique. Two simple models have been developed. The first model couples a spin 1/2 2D Ising magnetic lattice with to a 2D lattice of classic electric dipoles; this coupling is such that the change in the spin direction reorients a perpendicular component of the electric dipole neighbor of this same spin. Therefore, for this first model, the phase transitions of the magnetic and electric lattices occur at the same temperature, and the Hamiltonian is dependent of three parameters. For the second model, two lattices have been used again, a 2D Ising lattice for the magnetic system and an electric lattice that also behaves as a 2D Ising lattice. In this case, the coupling between the spin and the electric dipole occurs through a two-level system, generating the possibility of the independent transition temperatures for the two systems. This second model also contains three independent parameters
Mestrado
Física da Matéria Condensada
Mestre em Física
40
Fonseca, Jacyana Saraiva Marthes. "Zeros de Fisher e aspectos críticos do modelo de Ising dipolar." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/59/59135/tde-15062011-134917/.
Анотація:
Estudamos o comportamento crítico do modelo de Ising com interação dipolar, em redes bidimensionais regulares. Este modelo apresenta um cenário fenomenologicamente rico devido ao efeito de frustração causado pela competição entre as interações de troca do Ising puro e a interação dipolar. A criticalidade do modelo foi estudada a partir das relações de escala de tamanho finito para os zeros da função de partição no plano complexo da temperatura. Esta abordagem nunca foi utilizada no estudo do modelo em questão. Nosso estudo se baseia em simulações de Monte Carlo usando o algoritmo multicanônico. O objetivo deste trabalho é obter a temperatura crítica em função do acoplamento (razão entre as intensidades dos acoplamentos ferromagnético e dipolar) e construir uma parte do diagrama de fase do modelo. Diferentes partes do diagrama de fase ainda não apresentam indicações conclusivas a respeito da ordem das linhas de transição. Em particular, há evidências na literatura de um ponto tricrítico para no intervalo [0.90,1.00], mas sua localização precisa não é conhecida. Nossas simulações indicam que o ponto tricrítico não se localiza no intervalo acima. Nossos resultados mostraram que, para [0.89,1.10], a fase do tipo faixas com h=1 passa para a fase tetragonal através de uma transição de segunda ordem. A análise de FSS para os zeros da função de partição na variável temperatura, apresenta, para =1.20, uma transição de fase de segunda ordem e para =1.30, uma transição de fase de primeira ordem. Dessa forma, o ponto tricrítico ocorre somente entre =1.20 e 1.30. Realizamos um estudo complementar baseado na abordagem microcanônica e observamos duas transições de fase de segunda ordem para =1.20 e duas transições de fase de primeira ordem para =1.30, que indica a presença da fase nemática intermediária.We study the critical behavior of the dipolar Ising model on two-dimensional regular lattices. This model presents a phenomenologically rich scenario due to the effect of frustration caused by the competition between the pure Ising interaction and the dipolar one. To study the criticality of this model we apply finite size scaling relations for the partition function zeros in the complex temperature plane. The partition function zeros analysis has never been used before to study such model with long-range interactions. Our study relies on Monte Carlo simulations using the multicanonical algorithm. Our goal is to obtain the critical temperature as a function of the coupling (the ratio between the ferromagnetic and dipolar couplings) to construct a part of the phase diagram. Different parts of the phase diagram do not present a conclusive results about the order of the phase transition lines.In particular, there is evidence of a tricritical point for [0.90,1.00], but its precise location is unknown. Our simulations indicate that the tricritical point is not located in the above range. Our FSS analysis show that for =1.20 the striped-tetragonal transition is a second-order phase transition and for =1.30 it is a first-order one. Thus, the tricritical point must occur between =1.2 and =1.3. We have used a microcanonical approach to study the criticality of this model too. This approach indicates two second-order phase transitions for =1.20 and two first-order phase transitions for =1.30. Therefore, it presents evidences for the presence of an intermediate nematic phase.
41
Karlson, Ida. "The Ising Model on a Random Graph Applied to Interacting Agents on the Financial Market." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-1637.
Анотація:
In this thesis we present a model of the interacting agents on the financial market. The agents are represented by a non-Euclidean random graph, where each agent communicate with another with probability p, and the interaction according to the Ising Model. We investigate properties of the model by direct calculations for small graph sizes, and by perfect simulation for larger graph sizes. We also present a model for asset price variation by using the magnetization of the Ising model.
42
Zimmerman, Dan Simon. "A study of the Ising model on the hexagonal closed-packed lattice with competing interactions." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/27226.
Анотація:
A study is made of an Ising model on the hexagonal closed-packed lattice, with ferromagnetic interactions D between nearest-neighbor spins located in adjacent layers, and antiferromagnetic interactions J between nearest-neighbor spins located in the same layer.
The ground states of the model are studied for different values of the parameter κ = —J/D. For κ < 1/2 the ground states are ferromagnetic and for κ > 1/2 the ground state spin configurations consist of stacked identical layers, such that each layer is obtained by stacking rows of alternating spins. At the point (κ — 1/2,t = 0), where t = T/D, there exists a multitude of degenerate ground state spin configurations which are not stable for κ ≠ 1/2.
Mean-field theory and low temperature expansions are used to study the phase diagram at low temperatures. Mean-field theory predicts that (κ= 1/2, t = 0) is a multiphase point where an infinite sequence of modulated phases coincide. In the vicinity of the multiphase point, the mean-field phase diagram is found to be similar to the mean-field phase diagram of the three-dimensional ANNNI model near its multiphase point.
Low temperature expansions are performed to second order in x, where x = e [sup -2/t], around the phase boundary between the ferromagnetic and the modulated phases. In contrast to standard low temperature expansions, the complete contribution, to order x², is obtained by grouping the contributions from excitations which contribute to arbitrarily high orders in x. The phase boundary between the ferromagnetic and the modulated phases is found to coincide, to order x², with the line onto which Domany mapped a kinetic Ising model on the honeycomb lattice. This strongly suggests that the Domany line is a phase boundary in three-dimensions.
Mean-field theory shows that this Ising model contains a continuous minimum-energy surface. A renormalization group method which applies to models which contain continuous minimum-energy surfaces is used to analyze the phase transition between the paramagnetic and the modulated phases. The calculation is performed using a Landau-Ginzburg-Wilson Hamiltonian whose minimum-energy surface consists of a hexagon and which contains fourth-order invariants due to the lattice. The calculation shows that the Hamiltonian does not contain a stable fixed point. This suggests that the paramagnetic-modulated phase transition of this Ising model is a fluctuation-induced first-order transition.Science, Faculty of
Physics and Astronomy, Department of
Graduate
43
Tartas, Jean. "Computer simulation study of domain growth in the two-dimensional ferromagnetic spin-flip Ising model." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64103.
44
Kauppi, Renée. "Properties of cluster-size heterogeneity near the phase transition in the two-dimensional Ising model." Thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79646.
Анотація:
Two different definitions of cluster-size heterogeneity are investigated as well as correlation time of different quantities using the Metropolis algorithm and the Wolff algorithm. It is confirmed that the correlation time multiplied by the computation time is lower for the Wolff algorithm in an area around the critical temperature. It is also confirmed that one definition of the heterogeneity has a local maximum at the critical temperature where as the other has an abrupt change in derivative. The local maximum appears with L ≥ 64 and it is predicted but not verified that systems with L > 43 have such a maximum. The relationship between the number of distinct cluster sizes for clusters with spin-up and spin-down is investigated and it is observed that these transition from being significantly different at lower temperatures to being mostly similar at higher temperatures. The point of transition appears to be near the critical temperature.
45
Lin, Ming-Shr Matt Wilson R. M. Wilson R. M. "Applications of combinatorial analysis to the calculation of the partition function of the Ising Model /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05052009-133119.
46
Godoi, Marcos Roberto de. "Estudo do modelo Blume-Capel através da teoria de campo médio /." Rio Claro, 2019. http://hdl.handle.net/11449/190857.
Анотація:
Orientador: Makoto YoshidaResumo: Apresenta-se um estudo das transições de fase de um material ferromagnético representado pelo modelo Blume-Capel. A investigação é realizada através da teoria de campo médio implementada através da aproximação de Bethe-Peierls. Como tarefa preliminar é proposta uma revisão detalhada da aproximação de Weiss para investigação dos fenômenos críticos de sistemas magnéticos. Nesta etapa, tanto o modelo de Ising quanto o modelo Blume-Capel são considerados. Em seguida, uma revisão do modelo de Ising através da aproximação de Bethe-Peierls, tida como mais precisa, também é realizada e de posse da experiência adquirida, o modelo Blume-Capel é detalhadamente investigado.
Abstract: The study of the phase transition of Blume-Capel ferromagnet is carried out by means of Bethe-Peierls approximation. A detailed review of 2D Ising model and the Weiss/Bethe-Peierls mean field theory is presented as the preliminar task. This is followed by a review of Blume-Capel model and finally by the investigations of its critical phenomena in the Bethe-Peierls approximation.
Mestre
47
Wojtas, David Heinrich. "Structure and Diffraction Properties of Disordered Systems." Thesis, University of Canterbury. Electrical and Computer Engineering, 2011. http://hdl.handle.net/10092/5569.
Анотація:
In many systems of interest, both physical and biological, disorder inhibits the organization and cooperative properties of the system. Disorder can originate from a variety of system defects and the degree of disorder also varies. Geometric frustration introduces disorder into a system in which all the preferred interactions between the elements of the system cannot be satisfied due to the topology of an underlying lattice that describes the position of these elements. Recently, geometric frustration has been recognized as an important organizing principle in a diverse range of systems from superconducting networks to neural computation. The correlation behavior of such systems is often complicated and poorly understood. The myosin lattice of higher vertebrate muscle is a geometrically frustrated system, and the presence of this kind of disorder has prevented a rigorous interpretation of X-ray diffraction patterns from muscle fibres for the purposes of studying muscle molecular structure.
This thesis investigates the correlation behavior of two geometrically frustrated systems, the triangular Ising antiferromagnet (TIA) and the fully frustrated square Ising model (FFS), and its use to interpret X-ray fibre diffraction patterns. A combination of numerical evaluation of exact expressions and Monte Carlo simulation is used to study a number of aspects of the two-point correlation function of the TIA and FFS. In the case of the TIA, a simple functional expression is developed that allows accurate calculation of the correlation function. Theory is developed for calculating diffraction by polycrystalline fibres of helical molecules, in which the constituent crystallites contain correlated substitution disorder. The theory was used to study the characteristics of diffraction by fibres with TIA-type substitution disorder statistics. A quantitative model of the disorder in the myosin filament array is developed and the above theory is used to calculate X-ray fibre diffraction from low resolution models of the myosin filament array in higher vertebrate muscle. The calculated diffraction is compared to measured diffraction data, showing good agreement.
48
Pesheva, Nina Christova. "A mean-field method for driven diffusive systems based on maximum entropy principle." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54398.
Анотація:
Here, we propose a method for generating a hierarchy of mean-field approximations to study the properties of the driven diffusive Ising model at nonequilibrium steady state. In addition, the present study offers a demonstration of the practical application of the information theoretic methods to a simple interacting nonequilibrium system. The application of maximum entropy principle to the system, which is in contact with a heat reservoir, leads to a minimization principle for the generalized Helmholtz free energy. At every level of approximation the latter is expressed in terms of the corresponding mean—field variables. These play the role of variational parameters. The rate equations for the mean-field variables, which incorporate the dynamics of the system, serve as constraints to the minimization procedure.
The method is applicable to high temperatures as well to the low temperature phase coexistence regime and also has the potential for dealing with first-order phase transitions. At low temperatures the free energy is nonconvex and we use a Maxwell construction to find the relevant information for the system.
To test the method we carry out numerical calculations at the pair level of approximation for the 2-dimensional driven diffusive Ising model on a square lattice with attractive interactions. The results reproduce quite well all the basic properties of the system as reported from Monte Carlo simulations.Ph. D.
49
Juozapavicius, Ausrius. "Density-Matrix Renormalization-Group Analysis of Kondo and XY models." Doctoral thesis, KTH, Physics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3260.
50
Cannizzo, Andrea. "Mécanique statistique et thermodynamique de l'adhésion, des transformations de phase et de la rupture dans les micro et nanosystèmes." Electronic Thesis or Diss., Centrale Lille Institut, 2023. http://www.theses.fr/2023CLIL0027.
Анотація:
Les phénomènes de micro-instabilité et de multi-stabilité jouent un rôle clé dans divers systèmes mécaniques et physiques, tant artificiels que biologiques. Leur compréhension fait donc l'objet d'un vaste champ d'études, avec de nombreuses applications pratiques et théoriques. La modélisation de l'effet de la température sur les micro-instabilités, apparaissant dans différents phénomènes artificiels et biologiques, permet la validation de la mécanique statistique pour les petits systèmes, par la comparaison avec les données expérimentales obtenues à l'aide de la spectroscopie de force et d'essais micromécaniques, fournissant ainsi des informations utiles sur les réponses induites par les forces ou les allongements appliqués. Ces analyses sont particulièrement importantes pour l'étude de tous les systèmes qui présentent deux (ou plus) états métastables, tels que les processus d'adhésion/déadhésion, les transformations de phase (pliage/dépliage et phénomènes pseudo-élastiques) et la propagation des fissures et des fractures dans les systèmes à l'échelle nano- et micro-métriqe. À titre d'exemple, la température influence fortement les caractéristiques de transformation de phase des nanofils pseudo-élastiques utilisés comme actionneurs et capteurs en nanotechnologie, ou modifie les propriétés d'adhésion des cellules métastatiques dans les processus d'invasion du cancer. La réponse force-extension ou contrainte-déformation est l'une des principales caractéristiques utiles pour comprendre les effets des micro-instabilités et, pour l'obtenir analytiquement, il faut évaluer la fonction de partition du système, qui est l'outil essentiel de la mécanique statistique. Par conséquent, la forme complexe de l'énergie potentielle du problème étudié est approximée en utilisant la technique des variables de spin, ce qui permet d'obtenir une quantité discrète capable d'identifier les différents puits d'énergie potentielle. La première partie de cette thèse traite de l'état de l'art, des problèmes ouverts, des motivations et de la description des méthodologies adoptées. La partie suivante montre comment différents phénomènes physiques peuvent être étudiés par la même approche de modélisationMicro-instability and multi-stability phenomena play a key role in various mechanical and physical systems, both artificial and biological. As such, their understanding is addressed in a wide field of studies, with many practical and theoretical applications. The modeling of the temperature effect on micro-instabilities, appearing in different artificial and biological phenomena, allows the validation of the statistical mechanics for small systems, through the comparison with experimental data obtained using force spectroscopy and micromechanical testing, thus providing useful insights on the responses induced by applied forces or elongations. These analyses are particularly important in the study of all the systems that present two (or more) metastable states such as the adhesion/deadhesion processes, the phase transformations (e.g. the folding/unfolding and pseudo-elastic phenomena), and the cracks and fractures propagation in nano- and micro-scale systems. For example, the temperature strongly influences the phase transformation features of pseudo-elastic nanowires used as actuators and sensors in nanotechnology or modifies the adhesion properties of metastatic cells in cancer invasion processes. The force-extension or stress-strain response is one of the main useful features to understand the effects of micro-instabilities and, in order to be analytically obtained, one needs to evaluate the system partition function, which is the essential tool of statistical mechanics. Hence, the complex potential energy landscape of the problem under investigation is approximated using the spin variables technique, introducing a discrete quantity able to identify the different potential energy wells. The first part of this thesis addresses the state of the art, the open problems, the motivations, and the description of the adopted methodologies. The following part shows how commonly different physical phenomena can be studied by the same modeling approach