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Relevant bibliographies by topics / Ginzburg-Landau theory; Mean-field model

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Academic literature on the topic 'Ginzburg-Landau theory; Mean-field model'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Ginzburg-Landau theory; Mean-field model"

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DAVIS, R. L. "SUPERFLUID FIELD THEORY." International Journal of Modern Physics A 08, no. 28 (November 10, 1993): 5005–21. http://dx.doi.org/10.1142/s0217751x9300196x.

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The very low temperature dynamics of an isotropic superfluid is derived from a repulsive bosonic field theory. The field theory is a fully dynamical generalization of the Ginzburg-Landau theory, which at zero temperature has semiclassical superfluid solutions. It is shown that supercurrent quenching occurs above some intrinsic critical velocity. The speed of first sound is calculated and the Landau criterion for a maximum superfluid velocity is derived. At finite temperature, the thermodynamic potential is computed, the order parameter and gap equations are derived, the origin of the Landau two-fluid model is identified and the thermomechanical effect is explained. This theory successfully describes many of the features of 4He well below the critical temperature, as well as relativistic generalizations.

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Bonora, L., A. A. Bytsenko, M. Chaichian, and A. E. Gonçalves. "Elliptic genera and q-series development in analysis, string theory, and N=2 superconformal field theory." International Journal of Modern Physics A 34, no. 33 (November 30, 2019): 1950226. http://dx.doi.org/10.1142/s0217751x19502269.

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In this paper, we examine the Ruelle-type spectral functions [Formula: see text], which define an overall description of the content of the work. We investigate the Gopakumar–Vafa reformulation of the string partition functions, describe the [Formula: see text] Landau–Ginzburg model in terms of Ruelle-type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in [Formula: see text] theories, construct the functional equations for [Formula: see text], and analyze the modular transformation laws for the elliptic genus of the Landau–Ginzburg model and study their properties in details.

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FUCHS, JÜRGEN, and MAXIMILIAN KREUZER. "ON THE LANDAU–GINZBURG DESCRIPTION OF $(A_1^{(1)})^{\oplus N}$ INVARIANTS." International Journal of Modern Physics A 09, no. 08 (March 30, 1994): 1287–304. http://dx.doi.org/10.1142/s0217751x94000583.

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We search for a Landau–Ginzburg interpretation of nondiagonal modular invariants of tensor products of minimal n = 2 superconformal models, looking in particular at automorphism invariants and at some exceptional cases. For the former we find a simple description as Landau–Ginzburg orbifolds, which reproduces the correct chiral rings as well as the spectra of various Gepner type models and orbifolds thereof. On the other hand, we are able to prove for one of the exceptional cases that this conformal field theory cannot be described by an orbifold of a Landau–Ginzburg model with respect to a manifest linear symmetry of its potential.

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DZHUNUSHALIEV, VLADIMIR, and DOUGLAS SINGLETON. "GINZBURG–LANDAU EQUATION FROM SU(2) GAUGE FIELD THEORY." Modern Physics Letters A 18, no. 14 (May 10, 2003): 955–65. http://dx.doi.org/10.1142/s0217732303010776.

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The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

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Tuyen, Le Thi Cam, Bui Duc Tinh, Le Minh Thu, Nguyen Quang Hoc, and Nguyen Khac Man. "Fluctuation diamagnetic susceptibility in type-II superconductors under magnetic field." International Journal of Modern Physics B 34, no. 04 (December 20, 2019): 2050007. http://dx.doi.org/10.1142/s0217979220500071.

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Strong fluctuation effects were found in both low- and high-field regimes by recent measurements of magnetization on [Formula: see text] (LCCO) single crystals. The low-field fluctuation diamagnetic susceptibility data could not be fitted by simple Gaussian fluctuation theory using the lowest Landau level (LLL) approximation because of the slightly nonlinear behavior around the mean-field transition temperature [Formula: see text]. Self-consistent calculation of fluctuation diamagnetic susceptibility in high-temperature superconductors, based on the Ginzburg–Landau (GL) two-dimensional model and including all Landau levels, is presented. Our results are valid for arbitrary values of the magnetic field not too close to [Formula: see text]. The results agree well with the experimental data in a wide region around [Formula: see text], including both below and above [Formula: see text].

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Lim, Kok Geng, Khian Hooi Chew, Lye Hock Ong, and Makoto Iwata. "Recent Advances in Application of Landau-Ginzburg Theory for Ferroelectric Superlattices." Solid State Phenomena 232 (June 2015): 169–95. http://dx.doi.org/10.4028/www.scientific.net/ssp.232.169.

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Ferroelectric superlattices with polarization perpendicular to the surface or interface are studied within the framework of the Landau-Ginzburg theory. An interface energy is introduced in the free energy to describe the effect of mixing and local polarization coupling at interface. Internal electric field is considered in the model. For superlattices grown on substrate, the influence of substrate on the properties of ferroelectric superlattices is required. This brief review is a sequel to the previous review article [1], which summarizes the recent development in Landau-Ginzburg theory developed for studying ferroelectric superlattices over approximately the last three years.

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Contreras, Andres, and Xavier Lamy. "Persistence of superconductivity in thin shells beyond Hc1." Communications in Contemporary Mathematics 18, no. 04 (May 3, 2016): 1550047. http://dx.doi.org/10.1142/s0219199715500479.

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In Ginzburg–Landau theory, a strong magnetic field is responsible for the breakdown of superconductivity. This work is concerned with the identification of the region where superconductivity persists, in a thin shell superconductor modeled by a compact surface [Formula: see text], as the intensity [Formula: see text] of the external magnetic field is raised above [Formula: see text]. Using a mean field reduction approach devised by Sandier and Serfaty as the Ginzburg–Landau parameter [Formula: see text] goes to infinity, we are led to studying a two-sided obstacle problem. We show that superconductivity survives in a neighborhood of size [Formula: see text] of the zero locus of the normal component [Formula: see text] of the field. We also describe intermediate regimes, focusing first on a symmetric model problem. In the general case, we prove that a striking phenomenon we call freezing of the boundary takes place: one component of the superconductivity region is insensitive to small changes in the field.

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DI GREZIA, ELISABETTA, SALVATORE ESPOSITO, and ADELE NADDEO. "QUANTUM PHASE EXCITATIONS IN GINZBURG–LANDAU SUPERCONDUCTORS." International Journal of Modern Physics B 20, no. 06 (March 10, 2006): 737–45. http://dx.doi.org/10.1142/s021797920603353x.

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We give a straightforward generalization of the Ginzburg–Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb–Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity. A physical scenario behind the model proposed, which can be directly tested by experiments, is envisaged.

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DZHUNUSHALIEV, VLADIMIR, DOUGLAS SINGLETON, and DANNY DHOKARH. "Effective Abelian-Higgs Theory from SU(2) gauge field theory." International Journal of Modern Physics A 20, no. 15 (June 20, 2005): 3481–87. http://dx.doi.org/10.1142/s0217751x05026807.

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In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU (2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

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BULAEVSKII, L. N. "MACROSCOPICAL THEORY OF LAYERED SUPERCONDUCTORS." International Journal of Modern Physics B 04, no. 11n12 (September 1990): 1849–77. http://dx.doi.org/10.1142/s0217979290000905.

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The macroscopical Ginzburg-Landau models with effective-mass tensor and Josephson coupling of the layers are used to describe the magnetic properties of layered superconductors (dichalcogenides of transition metals and intercalated compounds, organic superconductors and high-Tc copper oxide compounds). In the framework of such models the magnetic critical fields, Abrikosov lattice, torque, Josephson oscillations, Gaussian fluctuations are considered and the validity of mean field theory in the model with Josephson coupling is discussed. The layeredcompounds with different superconducting layers are also studied including the dependence of critical temperature on the strength of coupling and temperature dependence of magnetic anisotropy. The experimental data of high-Tc superconductors are discussed to show that in Bi- and Tl-compounds the conditions of Josephson coupling of layers is fulfilled.

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Dissertations / Theses on the topic "Ginzburg-Landau theory; Mean-field model"

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Richardson, Giles William. "Vortex motion in type II superconductors." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320582.

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Calza, Thiago Cheble Alves. "Modelo de Ginzburg-Landau a partir da teoria de campos a temperatura finita." Universidade do Estado do Rio de Janeiro, 2015. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8735.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico
Neste trabalho, utilizamos o formalismo de teorias quânticas de campos a temperatura finita, tal como desenvolvidas por Matsubara, aplicado a uma hamiltoniana de N campos escalares com autointeração quártica a N grande. Obtém-se uma expressão, na primeira aproximação quântica, para o coeficiente do termo quadrático da hamiltoniana ("massa quadrada"), renormalizado, como função da temperatura. A partir dela, estudamos o processo de quebra espontânea de simetria. Por outro lado, a mesma hamiltoniana é conhecida como modelo de Ginzburg-Landau na literatura de matéria condensada, e que permite o estudo de transições de fase em materiais ferromagnéticos. A temperatura é introduzida através do termo quadrático na hamiltoniana, de forma linear: é proporcional à diferença entre a variável de temperatura e a temperatura crítica. Tal modelo, porém, possui validade apenas na regi~ao de temperaturas próximas à criticalidade. Como resultado de nossos cálculos na teoria de campos a temperatura finita, observamos que, numa faixa de valores em torno da temperatura crítica, a massa quadrática pode ser aproximada por uma relação linear em relação à variável de temperatura. Isso evidencia a compatibilidade da abordagem de Ginzburg-Landau, na vizinhança da criticalidade, com respeito ao formalismo de campos a temperatura finita. Discutimos também os efeitos causados pela presença de um potencial químico no sistema.
In this work, we use the formalism of quantum field theories at finite temperature, as developed by Matsubara, applied to a Hamiltonian of N scalar fields with quartic self-interaction at N large. We get an expression in the first quantum approximation to the coeficient of the quadratic term of the Hamiltonian ("square mass"), renormalized as a function of temperature. From it, we study the process of spontaneous symmetry breaking. On the other hand, the same Hamiltonian is known as Ginzburg-Landau model in the literature of condensed matter, and allows the study of phase transitions in ferromagnetic materials. The temperature is introduced through the quadratic term in the Hamiltonian of the linear form: is proportional to the difference between the temperature and the critical temperature. This model, however, is valid only in the region of temperatures close to criticality. As a result of our calculations in the field theory at finite temperature, we observed that in a range of values around the critical temperature, the quadratic mass can be approximated by a linear relation with the temperature. This highlights the compatibility of the Ginzburg-Landau approach, in the vicinity of criticality with respect to the formalism of finite temperature field. We also discuss the effects caused by the presence of a chemical potential in the system.

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Martins, Gabriel Weber. "O modelo de Landau-Lifshitz e a integrabilidade em teoria de cordas." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-15052012-150633/.

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Nesta tese, estudamos a integrabilidade quântica de modelos contínuos relevantes no contexto da quantização da supercorda do tipo IIB em AdS5 x S5, e, conseqüentemente, de interesse para a demonstração e uma melhor compreensão da correspondência AdS/CFT. Para os modelos de Landau-Lifshitz e de Alday-Arutyunov-Frolov, calculamos as amplitudes de espalhamento para três partículas e mostramos a fatorabilidade de suas matrizes S em primeira ordem não-trivial. Propomos também um novo método para a quantização de sistemas integráveis contínuos no exemplo do modelo de Landau-Lifshitz su(1;1). Nosso método fornece uma solução alternativa para o problema do ordenamento operatorial, bem como uma prescrição para a dedução das identidades de traço e do espectro das cargas quânticas conservadas. Ademais, mostramos que, por ser baseado em um processo de regularização e renormalização operatorial, concomitante à construção das extensões auto-adjuntas, a integrabilidade é preservada durante a quantização.
In this thesis, we study the quantum integrability of continuous models which arise from consistent truncations of type IIB superstring theory on AdS5 X S5, and, therefore are relevant for improving our current understanding of the AdS/CFT correspondence. For the Landau-Lifshitz and the Alday-Arutyunov-Frolov models, we compute the three-particle scattering amplitude and show the factorizability of the corresponding S matrices at the first non-trivial order. We also propose a new method for quantizing continuous integrable systems and apply it to the su(1;1) Landau-Lifshitz model. Our method provides an alternative solution to the longstanding operator ordering problem and gives a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. Moreover, since it is based on operator regularization and renormalization, as well as on the construction of the self-adjoint extensions, the integrability is preserved during the quantization process

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Troussaut-Bertrand, Francine. "Etude du KH2PO4 au voisinage du point tricritique : mesures de biréfringence sous pression et détermination des coefficients d'électrostriction." Grenoble 1, 1987. http://www.theses.fr/1987GRE10039.

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Mise en evidence de la possibilite d'etude des variations du parametre d'ordre, en fonction de la pression, de la temperature et du champ electrique, a partir de mesures de birefringence; confirmation de l'ordre de transition de rbh::(2)po::(4) et etude du diagramme de phases 3d de kh::(2)po::(4) au voisinage d'un point tricritique. Etude des proprietes electromecaniques de kh::(2)po::(4) par une nouvelle technique de diffraction simultanee neutron-gamma, dans le but de preciser la relation entre les variations du parametre d'ordre et les anomalies de la dilatation au voisinage de la transition; interpretation qualitative par un modele de type slater

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Books on the topic "Ginzburg-Landau theory; Mean-field model"

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Provatas, Nicholas. Phase-field methods in materials science and engineering. Weinheim: Wiley-VCH, 2010.

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Horing, Norman J. Morgenstern. Quantum Statistical Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.001.0001.

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The methods of coupled quantum field theory, which had great initial success in relativistic elementary particle physics and have subsequently played a major role in the extensive development of non-relativistic quantum many-particle theory and condensed matter physics, are at the core of this book. As an introduction to the subject, this presentation is intended to facilitate delivery of the material in an easily digestible form to students at a relatively early stage of their scientific development, specifically advanced undergraduates (rather than second or third year graduate students), who are mathematically strong physics majors. The mechanism to accomplish this is the early introduction of variational calculus with particle sources and the Schwinger Action Principle, accompanied by Green’s functions, and, in addition, a brief derivation of quantum mechanical ensemble theory introducing statistical thermodynamics. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green’s function equations of motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and non-equilibrium Green’s functions, and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions includes quantum plasma dynamic, nonlocal screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low-dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as superconductors, superfluids and graphene.

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Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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Book chapters on the topic "Ginzburg-Landau theory; Mean-field model"

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Zinn-Justin, Jean. "Abelian gauge theories: The framework of quantum electrodynamics (QED)." In Quantum Field Theory and Critical Phenomena, 507–47. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0021.

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This chapter is devoted Abelian gauge theory, whose physical realization is quantum electrodynamics (QED). Since many textbooks deal extensively with QED, the chapter focusses mainly on the more formal properties of Abelian gauge theories. First, the free massive vector field is considered, because its quantization does not immediately follow from the quantization of the scalar field, and thus requires a specific analysis. If the vector field is coupled to a conserved current, it is possible to construct a field theory with fermion matter renormalizable in four dimensions. In this case, a massless vector limit can be defined, and the corresponding field theory is gauge invariant. To directly quantize a gauge theory starting directly from first principles, it is necessary to introduce gauge fixing. The formal equivalence between different gauges is established. The Abelian gauge symmetry, broken by gauge-fixing terms, leads to a set of Ward–Takahashi (WT) identities which are used to prove the renormalizability of the quantum field theory (QFT). Renormalization group (RG) equations follow, and the RG β-function is calculated at leading order. As an introduction to the Standard Model of particle physics, the Abelian Landau–Ginzburg–Higgs model is described, where the gauge field is coupled to a complex scalar field with a non-zero expectation value, leading to a model that classically also describes a superconductor in a magnetic field.

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Swendsen, Robert H. "Phase Transitions and the Ising Model." In An Introduction to Statistical Mechanics and Thermodynamics, 423–46. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.003.0031.

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Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.

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Mussardo, Giuseppe. "Minimal Conformal Models." In Statistical Field Theory, 399–442. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0011.

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Chapter 11 discusses the so-called minimal conformal models, all of which are characterized by a finite number of representations. It goes on to demonstrate how all correlation functions of these models satisfy linear differential equations. It shows how their explicit solutions are given by using the Coulomb gas method. It also explains how their exact partition functions can be obtained by enforcing the modular invariance of the theory. The chapter also covers null vectors, the Kac determinant, unitary representations, operator product expansion, fusion rules, Verlinde algebra, screening operators, structure constants, the Landau–Ginzburg formulation, modular invariance, and Torus geometry. The appendix covers hypergeometric functions.

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Mussardo, Giuseppe. "Conformal Field Theories with Extended Symmetries." In Statistical Field Theory, 476–517. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0013.

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The conformal transformations may be part of a larger group of symmetry. Chapter 13 discusses several of the extensions of conformal field theory, including supersymmetry, Z N transformations and current algebras. It also covers superconformal models, the Neveu–Schwarz and Ramond sectors, irreducible representations and minimal models, additional symmetry, the supersymmetric Landau–Ginzburg theory, parafermion models, the relation to lattice models, Kac–Moody algebras, Virasoro operators, the Sugawara Formula, maximal weights and conformal models as cosets. The appendix provides for the interested reader a self-contained discussion on the Lie algebras, include the dual Coxeter numbers, properties of weight vectors and roots/simple roots.

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Eckle, Hans-Peter. "Phase Transitions, Critical Phenomena, and Finite-Size Scaling." In Models of Quantum Matter, 111–76. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0005.

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Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory of finite-size scaling. After surveying the basic notions of phases, phase diagrams, and phase transitions, this chapter focuses on critical behaviour at a second-order phase transition. The Landau-Ginzburg theory and the concept of scaling prepare readers for an elementary introduction to the concepts of the renormalization group, followed by an introduction into the field of quantum phase transitions where quantum fluctuations take over the role of thermal fluctuations.

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Ondrejkovic, P., P. Marton, V. Stepkova, and J. Hlinka. "Fundamental Properties of Ferroelectric Domain Walls from Ginzburg–Landau Models." In Domain Walls, 76–108. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862499.003.0004.

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This chapter discusses the contemporary possibilities, prospects, and limitations of phase-field simulations and Ginzburg-Landau-Devonshire models of DWs. It focuses on the most studied ferroelectric oxides BaTiO3, KNbO3, PbTiO3, as well as in various complex perovskite oxides like lead zirconate titanate (PZT) and lead-based relaxor ferroelectrics. In the past decade, there have been multiple important results published in the field of perovskite ferroelectrics with a support of phase-field simulations. Certain predictions, like existence of Bloch walls in BaTiO3 or vortex structures in PbTiO3-SrTiO3 superlattices have been verified by atomistic or ab-initio calculations. The chapter resumes their available model potentials and the key predictions reported in the last decade. It is complemented by original data allowing comparisons and an outlook.

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A.ANSELM, A. "A MODEL OF FIELD THEORY WITH NONVANISHING RENORMALIZED CHARGE." In Under the Spell of Landau, 526–34. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814436571_0051.

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FATEEV, V. A., and S. L. LYKYANOV. "THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY." In 30 Years of the Landau Institute — Selected Papers, 719–32. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814317344_0072.

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ZAMOLODCHIKOV, ALEXANDER B., and ALEXEY B. ZAMOLODCHIKOV. "Factorized S-Matrices in Two Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Theory Models." In 30 Years of the Landau Institute — Selected Papers, 559–97. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814317344_0065.

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Conference papers on the topic "Ginzburg-Landau theory; Mean-field model"

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Bittner, Elmar, Axel Krinner, and Wolfhard Janke. "Vortex-Line Percolation in a Three-Dimensional Complex Ginzburg-Landau Model." In XXIIIrd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2005. http://dx.doi.org/10.22323/1.020.0247.

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Kawai, Hiroki, and Yoshio Kikukawa. "A study of N=2 Landau-Ginzburg model by lattice simulation based on a Nicolai map." In The XXVIII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.105.0255.

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Schrade, David, Bai-Xiang Xu, Ralf Mu¨ller, and Dietmar Gross. "On Phase Field Modeling of Ferroelectrics: Parameter Identification and Verification." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-411.

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This contribution introduces a thermodynamically consistent, fully electro-mechanically coupled micro-mechanical model for ferroelectric materials. Adopting a phase field concept, in which the spontaneous polarization is used as order parameter, a Ginzburg-Landau type theory is formulated for the evolution of the order parameter. The equations are discretized within the scope of the Finite Element Method, and implicit time integration is used to solve the non-linear evolution equation. Examples illustrate the physical meaning of phase field parameters and give an application to multi-axial switching in which experimental results are used for comparison.

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Dhote, Rakesh, and Kamran Behdinan. "Isogeometric Analysis of 3D Dynamic Thermo-Mechanical Phase-Field Model for Cubic-to-Tetragonal Phase Transformations in Shape Memory Alloys." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50643.

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In this paper, we study the dynamic thermo-mechanical behaviors of 3D shape memory alloy (SMA) nanostructures using the phase-field (PF) model. The PF model is based on the Ginzburg-Landau theory and requires a non-convex free energy function for an adequate description of the cubic-to-tetragonal martensitic phase transformations. We have developed a model that includes domain walls, treated as a diffuse interface, which leads to a fourth-order differential equation in a strain-based order parameter PF model. Arising numerical challenges have been overcome based on an isogeometric analysis (IGA) framework. Microstructure morphology evolution and consequent thermo-mechanical properties have been studied on SMA nanostructures of different geometries. The numerical results are in agreement with experimental observations. The developed coupled dynamic model has provided a better understanding of underlying microstructures and behaviors, which can be used for development of better SMA-based devices.

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Agboola, Babatunde O., Theocharis Baxevanis, and Dimitris C. Lagoudas. "Thermodynamically Consistent Thermomechanical Modeling of Kinetics of Macroscopic Phase Transition in SMA Using Phase Field Theory." In ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/smasis2014-7555.

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Experimental observations have shown that polycrystalline NiTi wires, strips and tubes develop inelastic strain via nucleation and growth of macroscopic martensitic domains under mechanical loading. These domains consist of almost fully-transformed grains, which result from micro-domains that are formed at the grain-size level. Evolution of these macroscopic domains via transformation front propagation is accompanied by complex interactions between mechanical work, latent heat, heat transfer, and loading rates. These interactions could affect the performance reliability or controllability of the material when deployed. Therefore, modeling effort is necessary to describe these interactions so as to improve the design and application of SMA devices. A 3-D thermodynamically consistent thermomechanical macroscopic model, which is able to describe phase transition kinetics in shape memory alloys, is proposed in this work. The model employs a Ginzburg-Landau-type kinetic law resulting from the notion of configurational forces associated with the gradient of an order parameter (a field variable). As a first attempt to demonstrate the capability of the model, 1-D simplification of the model is implemented within a finite element framework. Kinetics of phase transition and the effects of heat production associated with the thermomechanical coupling on the stress-strain response of an SMA are examined. In particular, the roles of external loading rate and heat transfer boundary conditions on the stress-strain response are investigated for displacement-controlled loading. Results obtained are in good agreement with experimental trends.

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Landis, Chad M. "Phase Field Modeling of Ferroelectric Domain Wall Interactions With Charge Defects." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16184.

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The overall objective of this work is to develop a theoretical model that can track the evolution of the domain structures in ferroelectric crystals, which are responsible for the non-linear electromechanical behavior of these materials. To this end, a continuum thermodynamics framework is devised, and the theory falls into the class of phase-field or diffuse-interface modeling approaches. Here a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships. The approach is shown to yield the commonly accepted Ginzburg-Landau equation for the evolution of the polarization order parameter. Within the theory a form for the free energy is postulated that can be applied to fit the general elastic, piezoelectric and dielectric properties of a ferroelectric material near its spontaneously polarized state. Thereafter, a principle of virtual work is specified for the theory and is implemented to devise a finite element formulation. The theory and numerical methods are used to investigate the interactions of 180° and 90° domain walls with an array of charge defects and to determine the electromechanical pinning strength of the array on the walls.

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Morikawa, Okuto. "Numerical study of ADE-type $\mathcal{N}=2$ Landau-Ginzburg models." In 37th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2019. http://dx.doi.org/10.22323/1.363.0145.

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Usha, R., and I. Mohammed Rizwan Sadiq. "Weakly Nonlinear Stability Analysis of a Non-Uniformly Heated Non-Newtonian Falling Film." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37201.

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A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to non-uniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface-tension and thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A non-linear evolution equation is derived by applying the long-wave theory and the equation governs the evolution of a power-law film flowing down an inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature is decreasing in the downstream direction while it is less stable for increasing temperature along the plate. Weakly non-linear stability analysis using the method of multiple scales has been investigated and this leads to a secular equation of the Ginzburg-Landau type. The analysis shows that both supercritical stability and subcritical instability are possible for the film flow system. The results indicate the existence of finite-amplitude waves and the threshold amplitude and non-linear speed of these waves are influenced by thermocapillarity. The results for the dilatant as well as pseudoplastic fluids are obtained and it is observed that the result for the Newtonian model agrees with the available literature report. The influence of non-uniform heating of the film flow system on the stability of the system is compared with the stability of the corresponding uniformly heated film flow system.

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Djondjorov, Peter A., Vassil M. Vassilev, and Daniel M. Danchev. "Analytic solutions for the temperature-field behaviour of the Ginzburg-Landau Ising type mean-field model with Dirichlet boundary conditions." In 10TH JUBILEE INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. Author(s), 2019. http://dx.doi.org/10.1063/1.5099022.

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Hietanen, Ari, and Biagio Lucini. "Interface tension of 3d 4-states Potts model using the Wang-Landau algorithm." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0034.

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