aqora

Three-dimensional vertex model in statistical mechanics from Baxter-Bazhanov model

Zhan-Ning Hu, Bo-Yu Hou

arXiv:hep-th/9503037Journal of Statistical PhysicsFeb 1, 19960 citations

Yang-Baxter Equation and Quantum Enveloping Algebras

Zhong-Qi Ma

The exact solution of C.N. Yang's one-dimensional many-body problem with repulsive delta-function interactions and R.J. Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras. This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour. Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of referenceThe exact solution of C.N. Yang's one-dimensional many-body problem with repulsive delta-function interactions and R.J. Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras. This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour. Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of reference

WORLD SCIENTIFIC eBooksDec 1, 199361 citations

Yang-Baxter Algebras and Integrable Models in Field Theory and Statistical Mechanics

Hector J. de Vega

Springer series in synergeticsJan 1, 19851 citation

Quantum statistical mechanics

Mehran Kardar A

Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Cambridge University Press eBooksJun 7, 20070 citations

Integrable Models in Condensed Matter Physics

Natan Andrei

This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.

arXiv:cond-mat/9408101Feb 1, 199566 citations

Quantum and Classical Statistical Mechanics of the Integrable Models in 1 + 1 Dimensions

R. Bullough, D. J. Pilling, JUSSI TIMONEN +2 more

Research reports in physicsJan 1, 19900 citations

Integrable Systems in Statistical Mechanics

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