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Proceedings of the conference on exactly soluble models in statistical mechanics : historical perspectives and current status, Northeastern University, Boston 30-31 March 1996

C. Judson King, Fa Yueh Wu

Published Jan 1, 1997• 0 citations

Abstract

Some of the early history of exactly soluble models, E.H. Lieb the many faces of the chiral Potts model, H. Au-Yang and J.H.H. Perk star-triangle and star-star relations in statistical mechanics, R.J. Baxter knot theory and statistical mechanics, L.H. Kauffman star-star relation for the Potts model, C. King and F.Y. Wu finite temperature correlations of the Ising chain in a transverse field, S. Sachdev exact solutions of low-dimensional reaction-diffusion systems, A.M.R. Cadilhe et al the infinite-state Potts model and solid partitions of an integer, H.Y. Huang and F.Y. Wu exact evaluation of thermodynamic quantities for the integrable T-J chain, A. Klumper multilayer extension of two-dimensional solvable statistical models to three dimensions, V. Popkov a higher-level Bailey lemma, A. Schilling and S.O. Warnaar the Heisenberg chain as a dynamical model for protein synthesis - some theoretical and experimental results, G.M. Schutz free fermion conditions and the symmetries of integrability, C.-M. Viallet. (Part contents).

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Statistical models, Yang-Baxter equation and related topics : proceedings of the satellite meetings of STATPHYS-19, Tianjin, China, 8-10 August 1995 ; and Symmetry, statistical mechanical models and applciations : proceedings of the Seventh Nankai Workshop, Tianjin, China, 12-13 August 1995

Mo‐Lin Ge, Fa Yueh Wu

Part 1 Satellite meeting of Statphys-19: quantum domains in ferromagnetic anisotropic Heisenberg chains, F.C. Alcaraz et al algebraic solution of the coincidence problem for crystals and quasi crystals, M. Baake reflection equations and surface critical phenomena, M.T. Batchelor quantum field theories in terms of group-valued local fields - an overview, L.L. Chau U(1)-invariant local and integrable lattice formulation of the massive Thirring model, C. Destri dilute algebras and solvable lattice models, U. Grimm quantum group and the Hofstadter problem, Y. Hatsugai et al domain walls in the spin-S quantum Ising chain, M. Henkel mutual exclusion statistics in the exactly solvable model of the Mott metal-insulator transition, M. Kohmoto et al boundary Yang-Baxter in the RSOS/SOS representation, W.M. Koo and C. Ahn probability of phase separation and two point temperature correlation functions for the Bose gas with delta interaction, V.E. Korepin and A.R. Its the generalized chiral clock model and its phase diagram, H. Au-Yang and J.H.H. Perk stochastic reaction-diffusion processes, operator algebras and integrable quantum spin chains, G.M. Schutz vertex-face correspondence in elliptic solutions of the Yang-Baxter equation, Y. Shibukawa logarithmic anomalies of susceptibility for solvable models, M. Takahashi on chiral Hubbard model at strong interaction, D.F. Wang soluble free-fermion models in d dimensions, F.Y. Wu bosonization based on Bethe Ansatz equations and proof of the conformal conjecture, Y.S. Wu and Y Yu. Part 3 The seventh Nankai workshop: one dimensional lattice models of electrons with r2 hopping and exchange, Ch. Gruber and D.F. Wang symmetry group invariants for spontaneous magnetization, J.-M. Maillard Zamolodchikov-Faddeev algebra vertex models, H.-P. Eckle scaling properties of the Ising model in a field, U. Grimm and B. Nienhuis experimental realizations of integrable reaction-diffusion processes in biological and chemical systems, G.M. Schutz and other papers. (Part contents).

WORLD SCIENTIFIC eBooksJan 1, 19960 citations

Yang-Baxter Equations in Paris : proceeding of the conference, Jussieu July 24-30, 1992

J.-M. Maillard

Exact Spectrum of the Critical Three-State Potts Chain (G Albertini) New Results Related to the Chiral Potts Model (H Au-Yang & J H H Perk) Chiral Potts Model: Corner Transfer Matrices and Parametrizations (R J Baxter) Solvable Lattice Models in Three Dimensions (VV Bazhanov) Dressing Symmetries (D Bernard) Knot Theory and Chem-Simons Lagrangian: Some Remarks about the corresponding Diagrams (P Cartier) Recent Progress in 2-D Quantum Gravity (V Dotsenko) On Coordinate Algebras of Quantum Groups at Root of Unity (B Enriquez) Integrability in Discrete Systems (B Grammaticos) New Construction of Solvable RSOS Models (S 0 Warnaar) Birational Automorphisms and Yang-Baxter Equations (J-M Maillard) Yang-Baxter Equations and Non-Commutative Differential Calculus (G Maltsiniotis) Physics Beyond Quasi-Particules: Spectrum and Completeness of the Three-State Superintegrable Chiral Potts Model (B M McCoy) Analytic Calulation of Conformal Weights for A-D-E Lattice Models (P Pearce) Quantum Tops (A Reiman) Remarks on Quasi-Hopf Algebras (M Rosso) Symmetries of the Yang-Baxter Equations: A Remarkable Family of Discrete Groups (C-M Viallet) The Yang-Baxter Equation in Knot Theory (F Y Wu).

WORLD SCIENTIFIC eBooksJan 1, 19930 citations

STATPHYS 19 : the 19th IUPAP International Conference on Statistical Physics, Xiamen, China, July 31-August 4, 1995

Bai-Lin Hao

Remarks on the development of statistical mechanics, C.N. Yang relativistic Bethe Ansatz and its applications, A. Zamolodchikov knots and statistical physics, F.Y. Wu correlation functions of exactly solvable models of statistical mechanics, V. Korepin type II superconductivity, D.A. Huse bose glass phase and vertex entanglement in superconductors, D. Nelson problems in self-assembling systems - from weak aggregates to biological membranes, M. Schick statistical mechanics of self-avoiding surfaces and membranes, F. David statistical problems in knot theory and noncommutative random walks, S. Nechaev universality in properties of disordered and chaotic systems, B. Alt'shuler. (Part Contents).

WORLD SCIENTIFIC eBooksJan 1, 19962 citations

Advanced Statistical Mechanics

Barry M. McCoy

Abstract This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on general theory which includes a summary of the basic principles of statistical mechanics; a presentation of the physical phenomena covered and the models used to discuss them; theorems on the existence and uniqueness of partition functions; theorems on order; and critical phenomena and scaling theory. The second part is on series and numerical methods which includes derivations of the Mayer and Ree–Hoover expansions of the low density virial equation of state; Groeneveld's theorems; the application to hard spheres and discs; a summary of numerical studies of systems at high density; and the use of high temperature series expansions to estimate critical exponents for magnets. The third part covers exactly solvable models which includes a detailed presentation of the Pfaffian methods of computing the Ising partition function, magnetization, correlation functions, and susceptibility; the star-triangle (Yang–Baxter equation); functional equations and the free energy for the eight-vertex model; and the hard hexagon and chiral Potts models. All needed mathematics is developed in detail and many open questions are discussed. The goal is to guide the reader to the current forefront of research.

Dec 1, 200999 citations

Classical and Quantum Nonlinear Integrable Systems

Preface (A Kundu) A Journey Through the KdV Equation (M Lakshmanan) The Painleve methods (R Conte and M Musette) Discrete Integrability (K M Tamizhmani, A Ramani, B Grammaticos and T Tamizhmani) The D-BAR Method: A Tool for Solving Two-Dimensional Integrable Evolution PDEs (A S Fokas) Introduction to Solvable Lattice Models in Statistical and Mathematical Physics (T Deguchi)II. QUANTUM SYSTEMS Unifying Approaches in Integrable Systems: Quantum and Statistical, Ultralocal and Nonultralocal (A Kundu) The Physical Basis of Integrable Spin Models (I Bose) Exact Solvability in Contemporary Physics (A Foerster, J Links and H-Q Zhou) The Thermodynamics of the spin-1/2 XXX Chain: Free Energy and Low-temperature Singularities of Correlation Lengths (A Klumper and C Scheeren) Reaction-Diffusion Processes and Their Connection with Integrable Quantum Spin Chains (M Henkel)

Taylor & Francis eBooksSep 1, 200319 citations

Introduction

M. Gaudin

From the exact solution of the Ising model by Onsager in 1944 up to that of the hard hexagon model by Baxter in 1980, the statistical mechanics of two-dimensional systems has been enriched by a number of exact results. One speaks (in quick manner) of exact models once a convenient mathematical expression has been obtained for a physical quantity such as the free energy, an order parameter or some correlation, or at the very least once their evaluation is reduced to a problem of classical analysis. Such solutions, often considered as singular curiosities upon their appearance, often have the interest of illustrating the principles and general theorems rigorously established in the framework of definitive theories, and also enabling the control of approximate or perturbative methods applicable to more realistic and complex models. In the theory of phase transitions, the Ising model and the results of Onsager and Yang have eminently played such a reference role. With the various vertex models, the methods of Lieb and Baxter have extended this role and the collection of critical exponents, providing new useful elements of comparison with extrapolation methods, and forcing a refinement of the notion of universality. Intimately linked to two-dimensional classical models (but of less interest for critical phenomena), one-dimensional quantum models such as the linear magnetic chain and Bethe's famous solution have certainly contributed to the understanding of fundamental excitations in many-body systems. One could also mention the physics of one-dimensional conductors.

Cambridge University Press eBooksMar 6, 20140 citations