About the book: This volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega.
About the book: This volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega.
About the book: This volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega.
Exact steady states of asymmetric diffusion and two-species annihilation with back reaction from the ground state of quantum spin models, F.C. Alcaraz Schrodinger invariance in discrete stochastic systems, M. Henkel and G. Schutz explicit thermostatics of Stanley's n-vector model on the harmonic chain by Fourier analysis, G. Junkel and H. Leschke non-Hermitian tricriticality in the Blume-Capel model with imaginary field, G. von Gehlen fusion of A-D-E lattice models, Y.-K. Zhou and P.A. Pearce a critical Ising model on the labyrinth, M. Baake et al Ising-like quantum chains with local supersymmetry, T.H. Baker and P.D. Jarvis q-deformations of quantum spin chains with exact valence-bond ground states, M.T. Batchelor and C.M. Yung the tensor product of tensor operators over quantum algebras - some applications to quantum spin chains, M. Scheunert infinite families of gauge-equivalent R-matrices and gradations of quantized affine algebras, A.J. Bracken et al sigma models with (2,2) world sheet supersymmetry, F. Delduc and E. Sokatchev. (Part Contents).
General principles of statistical mechanics, P.A. Pearce the connection between statistical mechanics and quantum field theory, B.M. McCoy two-dimensional models in statistical mechanics, R.J. Baxter topics in conformal field theory, C. Itzykson quantum gravity as dynamical triangulation, A.A. Migdal lattice gauge theory, C.J. Hamer quantum groups for physicists, M. Gould chaos versus order in Hamiltonian dynamical systems, G.R.W. Quispel quantum and classical integrable systems and statistical mechanics, R.K. Bullough and J.T. Timonen introduction to quantum field theory, R.J. Crewther.
This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text.
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).
Abstract This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background is provided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensive learning of the many facets of the subject.