Relevant bibliographies by topics / General Ising model

Academic literature on the topic 'General Ising model'

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Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "General Ising model"

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LIN, K. Y., and F. Y. WU. "GENERAL 8-VERTEX MODEL ON THE HONEYCOMB LATTICE: EQUIVALENCE WITH AN ISING MODEL." Modern Physics Letters B 04, no. 05 (March 10, 1990): 311–16. http://dx.doi.org/10.1142/s0217984990000398.

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It is shown that the general 8-vertex model on the honeycomb lattice is always reducible to an Ising model in a nonzero but generally complex magnetic field. In the most general case of the staggered 8-vertex model characterized by 16 independent vertex weights, the equivalent Ising model has three anisotropic interactions and a staggered magnetic field which assumes two different values on the two sublattices.
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KOLESÍK, M., and L. ŠAMAJ. "SOLVABLE CASES OF THE GENERAL SPIN-ONE ISING MODEL ON THE HONEYCOMB LATTICE." International Journal of Modern Physics B 06, no. 09 (May 10, 1992): 1529–38. http://dx.doi.org/10.1142/s0217979292000724.

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We consider a general spin-1 Ising model on the honeycomb lattice and propose a systematic method for obtaining its solvable cases. The method is based on a sequence of transformations which produces a path between the spin-1 and spin-½ Ising models. Considering necessary conditions for performing the transformations and the solvability of the resulting spin-½ system, we recover the known and find some new nontrivial ‘exactly solvable’ subspaces in the parameter space of the spin-1 Ising model.
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Morita, Tohru, and Kazuyuki Tanaka. "Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex Model." Journal of the Physical Society of Japan 62, no. 3 (March 15, 1993): 873–79. http://dx.doi.org/10.1143/jpsj.62.873.

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Li, Zhongyang. "Constrained percolation, Ising model, and XOR Ising model on planar lattices." Random Structures & Algorithms 57, no. 2 (May 7, 2020): 474–525. http://dx.doi.org/10.1002/rsa.20924.

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Brierley, Richard. "Ising model for strings." Nature Physics 16, no. 10 (October 2020): 1006. http://dx.doi.org/10.1038/s41567-020-01065-3.

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Ito, N., M. Taiji, and M. Suzuki. "CRITICAL DYNAMICS OF THE ISING MODEL WITH ISING MACHINE." Le Journal de Physique Colloques 49, no. C8 (December 1988): C8–1397—C8–1398. http://dx.doi.org/10.1051/jphyscol:19888641.

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LEE, S. F., and K. Y. LIN. "SPONTANEOUS MAGNETIZATION OF THE ISING MODEL ON THE GENERAL UTIYAMA LATTICE." Modern Physics Letters B 07, no. 29n30 (December 30, 1993): 1903–10. http://dx.doi.org/10.1142/s0217984993001910.

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The spontaneous magnetization of the two-dimensional Ising model on the general Utiyama lattice is derived exactly. Our results include the checkerboard, kagome, 4–8, and 3–12 lattices as special cases.
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Gonçalves, J. R., J. Poulter, and J. A. Blackman. "±J Ising model in 2D and of general composition." Journal of Magnetism and Magnetic Materials 140-144 (February 1995): 1701–2. http://dx.doi.org/10.1016/0304-8853(94)00631-8.

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Coutinho, S., F. C. SáBarreto, and R. J. Vasconcelos dos Santos. "Ising model randomly decorated with general spin angular momentum." Physica A: Statistical Mechanics and its Applications 196, no. 3 (June 1993): 461–75. http://dx.doi.org/10.1016/0378-4371(93)90209-m.

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Nakamura, Morikazu, Kohei Kaneshima, and Takeo Yoshida. "Petri Net Modeling for Ising Model Formulation in Quantum Annealing." Applied Sciences 11, no. 16 (August 18, 2021): 7574. http://dx.doi.org/10.3390/app11167574.

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Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.
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Dissertations / Theses on the topic "General Ising model"

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Valani, Yogendra P. "On the partition function for the three-dimensional Ising model." Thesis, City University London, 2011. http://openaccess.city.ac.uk/11667/.

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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.
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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.

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Чумак, Анна Вадимівна. "Моделі фінансового ринку на основі агентського підходу." Master's thesis, КПІ ім. Ігоря Сікорського, 2019. https://ela.kpi.ua/handle/123456789/33084.

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Магістерська дисертація виконана на 90 сторінках, містить 12 ілюстрацій, 22 таблиць та 20 джерел. У дисертації досліджується проблема моделювання фінансових ринків. Завдання моделювання є складною проблемою, особливо у випадках, коли фінансові часові ряди демонструють фрактальні властивості. У зв'язку з виниклою незгодою теорії рівноваги за Вальрасом і статистичними закономірностями, що з'являються при дослідженні сучасних даних, розглядаються нові методи аналізу фінансових ринків — агентсько-орієнтоване моделювання та фрактальний аналіз часових рядів. Мета дослідження – дослідити агентсько-орієнтоване моделювання та довести доцільність подальшого використання як інструмента аналітиків, трейдерів та інших осіб, що приймають рішення. Об’єкт дослідження – сучасні моделі фінансового ринку. Предмет дослідження – агентські підході фінансового ринку. Методи дослідження – аналіз моделей, порівняння розробленої поведінки з реальними фінансовими даними. У роботі розглядаються дві агентсько-орієнтовані моделі фондового ринку — модель Сато-Такаясу й узагальнена модель Ізінга.
The master's thesis consists of 88 pages, contains 12 illustrations, 25 tables and 20 sources. The dissertation explores the problem of financial markets modeling. Modeling is a complex problem, especially in cases where financial time series exhibit fractal properties. Due to the disagreement of Walras equilibrium theory and statistical regularities that emerge in the study of current data, new methods of financial market analysis are considered - agent-oriented modeling and fractal time series analysis. The purpose of the study is to investigate agency-oriented modeling and to prove the feasibility of further use as a tool by analysts, traders and other decision-makers. The object of study - modern models of the financial market. The subject of the study - the agency approaches to the financial market. Research methods - model analysis, comparison of developed on-line behavior with real financial data. Two agent-oriented stock market models are considered in the paper - the Sato-Takayasu model and the generalized Ising model.
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Nielsen, Morten. "Numerical studies of Ising models defined on a random lattice as applied to the phase behaviour of lipid bilayer systems." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35924.

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We examine complex fluid systems where both translational and conformational degrees of freedom are present and focus on systems in which the interplay between the two sets of degrees of freedom is manifested in the macroscopic phase behaviour. We develop an efficient random lattice algorithm describing the translational degrees of freedom and analyze a series of microscopic models defined on a two dimensional fluid surface. Different degrees of complexity in the description of the microscopic coupling between the translational and conformational degrees of freedom allow us to study a variety of models related to pure lipid membrane and lipid-sterol membrane systems.
The phase equilibrium described by the models is calculated by use of Monte Carlo simulation techniques. The different models are shown to exhibit a rich phase behaviour. Depending on the specific model parameters, the phase transition associated with the conformational degrees of freedom is found to be either coupled to, or uncoupled from, that associated with the conformational degrees of freedom.
Specifically, the order-disorder transition of an Ising model defined on a fluid surface is shown to be of first order, when the two sets of degrees of freedom are strongly coupled. In contrast, the transition falls in the universality class of the two-dimensional Ising model when the two sets of degrees of freedom are weakly coupled.
We next analyze a model for pure lipid bilayers which is shown to exhibit a phase behaviour with different types of macroscopic coupling between the two sets of degrees of freedom. Depending on the strength of the microscopic interactions the lipid chain melting transition and the lattice melting transition may be either macroscopically coupled or uncoupled.
A related model for lipid-sterol mixtures is shown to provide a consistent interpretation of the various phases of lipid-cholesterol and lipid-lanosterol binary mixtures based on the microscopic dual action of the sterol molecule on the lipid-chain degrees of freedom. We discuss the results for the systems in the context of membrane evolution and suggest that evolution has tended to optimize the lipid-sterol interaction so as to stabilize optimally the mechanical properties of the membrane. Furthermore, a specific small-scale structure is identified and characterized in the liquid-ordered phase in lipid-cholesterol mixtures. This structure is found to be absent in lipid-lanosterol mixtures.
Finally, a model for membrane lysis gives evidence for the high mechanical stabilizing effect of cholesterol on the membrane. The inclusion of cholesterol is shown to inhibit lysis whereas lanosterol only has little stabilizing effect.
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Books on the topic "General Ising model"

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1973-, Warzel Simone, ed. Random operators: Disorder effects on quantum spectra and dynamics. Providence, Rhode Island: American Mathematical Society, 2015.

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O, Seppäläinen Timo, ed. A course on large deviations with an introduction to Gibbs measures. Providence, Rhode Island: American Mathematical Society, 2015.

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1975-, Sims Robert, and Ueltschi Daniel 1969-, eds. Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I: American Mathematical Society, 2011.

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Book chapters on the topic "General Ising model"

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Ioffe, Dmitry. "Extremality of the Disordered State for the Ising Model on General Trees." In Trees, 3–14. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9037-3_1.

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Markström, Klas. "From the Ising and Potts Models to the General Graph Homomorphism Polynomial." In Graph Polynomials, 123–38. Boca Raton : CRC Press, [2017] | Series: Discrete mathematics and its applications: Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/9781315367996-7.

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Mussardo, Giuseppe. "Thermodynamic Bethe Ansatz." In Statistical Field Theory, 791–835. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0020.

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The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation. It discusses Casimir energy, Bethe relativistic wave function, the derivation of thermodynamics, the meaning of pseudo-energy (dressed energy and momentum), infrared and ultraviolet limits, the coefficient of bulk energy, the general form of the TBA equations, the thermodynamics of the free field theories, L-channel quantization and the LeClair–Mussardo formula. It also covers the application of the Yang–Lee S-matrix, the magnetic field Ising model, and the tricritical Ising model.
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Kobe, Sigismund, and Jarek Krawczyk. "Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses." In Computational Complexity and Statistical Physics. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195177374.003.0013.

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The previous three chapters have focused on the analysis of computational problems using methods from statistical physics. This chapter largely takes the reverse approach. We turn to a problem from the physics literature, the spin glass, and use the branch-and-bound method from combinatorial optimization to analyze its energy landscape. The spin glass model is a prototype that combines questions of computational complexity from the mathematical point of view and of glassy behavior from the physical one. In general, the problem of finding the ground state, or minimal energy configuration, of such model systems belongs to the class of NP-hard tasks. The spin glass is defined using the language of the Ising model, the fundamental description of magnetism at the level of statistical mechanics. The Ising model contains a set of n spins, or binary variables si, each of which can take on the value up (si = 1) or down (si= 1).
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Mussardo, Giuseppe. "One-dimensional Systems." In Statistical Field Theory, 48–105. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0002.

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Chapter 2 discusses one-dimensional statistical models, for example, the Ising model and its generalizations (Potts model, systems with O(n) or Zn-symmetry, etc.). It discusses several methods of solution and covers the recursive method, the transfer matrix approach, and series expansion techniques. General properties of these methods, which are valid on higher-dimensional lattices, are also covered. The contents of this chapter are quite simple and pedagogical but extremely useful for understanding the following sections of the book. One of the appendices at the end of the chapter is devoted to a famous problem of topology, i.e. the four-colour problem, and its relation with the two-dimensional Potts model.
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Mussardo, Giuseppe. "Form Factors and Correlation Functions." In Statistical Field Theory, 744–88. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0019.

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At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.
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Sornette, Didier. "Positive Feedbacks." In Why Stock Markets Crash. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175959.003.0004.

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This chapter examines the main mechanisms leading to positive feedbacks, that is, self-reinforcement, such as imitative behavior and herding between investors. It shows that positive feedbacks contribute to the development of speculative bubbles, preparing the instability for a major crash. After providing an overview of feedbacks and self-organization in economics, the chapter explains how positive feedback on prices can arise due to hedging of derivatives and investment strategies with an “insurance portfolio.” It then describes a general mechanism for positive feedback, known as the “herd” or “crowd” effect, based on imitation processes. It also presents empirical evidence of herding by financial analysts and the relationship between “anti-imitation” and self-organization before concluding with an analysis of cooperative behaviors resulting from imitation, focusing on the Ising model of cooperative behavior and the complex evolutionary adaptive systems of boundedly rational agents.
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Chimowitz, Eldred H. "The Renormalization-Group Method." In Introduction to Critical Phenomena in Fluids. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195119305.003.0012.

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The renormalization-group (RG) method discussed in this chapter has assumed a pivotal role in the modern theory of critical phenomena. It attempts to relate the partition function of a given system to that of a “similar system” with decreased degrees of freedom through a process referred to as renormalization. Exactly how these degrees of freedom are removed from the system, what we mean by a “similar” system, and how successive systems are coupled to one another are essentially the questions we take up in the introductory treatment given in this chapter. The RG method is a topic with large scope and found widely disseminated in an extensive physics literature on the topic; however, it is seldom found in engineering journals. Our purpose here is to try and make sense of some basic ideas with the RG approach so that it is more accessible to this wider community. For this we often rely upon some prior exposes of the subject in more specialized settings [1, 2, 3, 5]. In its complete sense, the RG method has only been made to work, at least analytically, for a few simple statistical-mechanical models. But aside from these numerical results, many important and quite general insights about critical phenomena can be developed from studying this approach to the problem, especially the central role played by length scale as a factor in describing the phenomenology. These ideas have significantly enhanced our understanding of ideas like scale invariance, universality classes, relevant scaling fields (as opposed to irrelevant ones), Hamiltonian renormalization, and so on; these and related concepts lie at the center of modern discourse on the subject. The essential concepts of the approach can be well illustrated using the Ising system since, with this model, lattice spins are fixed in space, which makes the analytical work quite transparent. This approach, called real space renormalization, is the RG method studied in this chapter.
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Zinn-Justin, Jean. "Critical phenomena: General considerations. Mean-field theory (MFT)." In Quantum Field Theory and Critical Phenomena, 324–56. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0014.

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This chapter is devoted to a brief review of general properties of phase transitions in macroscopic physics and, in particular in lattice models. Some of these lattice models actually appear as lattice regularizations of Euclidean (imaginary time) quantum physics theory (QFT). Most of the transitions considered in this work have the following character: spins on the lattice, or macroscopic particles in the continuum, interact through short-range forces, assumed, for simplicity, to decay exponentially. For simple systems, it is possible to find a local observable, called order parameter, whose expectation values depend on the phase in the several phase region, for example, the spin in ferromagnetic systems. In the disordered phase, the connected two-point function decreases exponentially at large distance, at a rate characterized by the correlation length (the inverse of the smallest physical mass in particle physics). In continuous transitions, the correlation length diverges at the critical temperature. Within the mean-field approximation (consistent with Landau's theory of critical phenomena), it can be shown that the singular behaviour of thermodynamic quantities at the critical temperature is universal. These properties can also be reproduced by calculating correlation functions with a perturbed Gaussian measure. It is then shown that the leading corrections to the mean-field approximation, in Ising-like systems, diverge at the critical temperature for dimensions smaller than or equal to $4$.
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Conference papers on the topic "General Ising model"

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Napolitano, George M., and Tatyana S. Turova. "Critical line of the Ising model on 2-dimensional CDT and its dual." In Proceedings of the MG14 Meeting on General Relativity. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813226609_0515.

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