2 edition of Statistical models, Yang-Baxter equation and related topics found in the catalog.
Statistical models, Yang-Baxter equation and related topics
Includes bibliographical references and index.
|Other titles||Symmetry, statistical mechanical models and applciations.|
|Statement||editors, M.L. Ge, F.Y. Wu.|
|Contributions||Ge, M. L., Wu, F. Y.|
|LC Classifications||QC174.7 .S743 1996|
|The Physical Object|
|Pagination||xiii, 444 p. :|
|Number of Pages||444|
|LC Control Number||97109545|
In Statistical models, Yang-Baxter equation and related topics, and Symmetry, statistical mechanical models and applications (Tianjin, ), pages 13– World Sci. Publishing, River Edge, NJ, Cited by: Special emphasis is given on the relations between these areas and in particular on topics where a mixture of methods (involving these theories) has been used. Some topics of particular interest are: group rings, unit groups, (graded) rings and also various algebraic structures used in the context of the Yang-Baxter Equation.
Two closely related methods: the Bethe ansatz approach, in its modern sense, based on the Yang–Baxter equations and the quantum inverse scattering method provide quantum analogs of the inverse spectral methods. These are equally important in . Yang-Baxter equation in quantum theory and statistical mechanics Set-theoretical solutions of quantum Yang-Baxter equation: E.K. Sklyanin Classical limits of SU(2)-invariant solutions of the Yang-Baxter equation. J. Soviet Math. 40 (), no. 1, 93– V.G. Drinfeld On some unsolved problems in File Size: KB.
This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes a extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward. Dilute Algebras and Solvable Lattice Models Published in Proceedings of the Satellite Meeting of STATP "Statistical Models, Yang-Baxter Equation and Related Topics", Tianjin Cited by: 7.
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Statistical Models, Yang-Baxter Equation and Related Topics - Proceedings of the Satellite MEeting of STATPHYS; Symmetry, Statistical, Mechanical Models and Applications - Proceedings of the Seventh Nankai WorkshopAuthor: M. The central theme of the two conferences, which drew participants from 18 countries, was the Yang–Baxter equation and its development and applications.
With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in.
Get this from a library. Statistical models, Yang-Baxter equation and related topics: proceedings of the Satellite Meeting of STATPHYS, Tianjin, China, August, ; and, Symmetry, statistical mechanical models and applications: proceedings of the Seventh Nankai Workshop, Tianjin, China, August, [M L Ge; F Y Wu;] -- This book contains the proceedings of two international.
Get this from a library. Statistical models, Yang-Baxter equation and related topics: proceedings of the Satellite Meeting of STATPHYS, Tianjin, China, August, ; and, Symmetry, statistical mechanical models and applications: proceedings of the Seventh Nankai Workshop, Tianjin, China, August, [M L Ge; F Y Wu;].
This book is Yang-Baxter equation and related topics book to "Exactly solved models in Statistical Physics" like Newton's Principa to classical mechanics or Gauss' "Disquisitiones arithmetica" to the theory of numbers or Kant's "Criticismn of pure Reason" to philosophy. Like Kant RJ Baxter may not be the founder of the field, but he was the one whoCited by: General form of the parameter-dependent Yang–Baxter equation.
Let be a unital associative its most general form, the parameter-dependent Yang–Baxter equation is an equation for (, ′), a parameter-dependent element of the tensor product ⊗ (here, and ′ are the parameters, which usually range over the real numbers ℝ in the case of an additive parameter, or over positive.
is a solution of (a2) if and Statistical models if is a solution of (a4), where is the -matrix, which switches the two factors of.
The Yang–Baxter equation (a2) can be interpreted as a condition on the interaction of relativistic particles with internal state space.Let the interaction between two particles with rapidities be given by ; then the Yang–Baxter equation. The Yang-Baxter Equation. I find that Polyakov model I described last time to be a great example of all sort of things: solitons, instantons, anyons, nonlinear sigma models, gauge theories, and topological quantum field theories all in one.
But I want to get back to braids plain and simple and introduce the Yang-Baxter equations. Figure 3: Star-triangle equation. Moves of type II, for which one strand crosses twice over another strand, can be reformulated for braids, namely that an over-crossing is the inverse of an under-crossing.
The Reidemeister move of type III is a precursor of the more general Yang–Baxter moves and can be represented also by the deﬁning. This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory.
ject of our presentation is the Yang–Baxter equation, one of the main objects in Quantum inverse scattering method (see ) and in exactly solvable models in Lattice Statistical Mechanics (see ). The approach we follow here is an algebro-geometric one, and. The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.
Yang, and in statistical mechanics, in R. Baxter’s work. 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 pioneering textbook attempts to make accessible results in this rapidly-growing area of by: 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 : Giuseppe Mussardo.
INTRODUCTION TO THE STATISTICAL PHYSICS OF INTEGRABLE MANY-BODY SYSTEMS Including topics not traditionally covered in the literature, such as (1 +1)-dimensional quantum ﬁeld theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied.
The Yang-Baxter equation is a central equation for integrability of models of statistical mechanics, where it can be used to solve a model through the use of the commuting transfer matrix method. $\begingroup$ I do not really work in this part of the field, but my very vague impression is that they are primarily useful in finding exact solutions for lattice models for statistical systems in 2D.
These "integrable models" may or may not have much direct relevance to the real world, but are theoretically interesting, as most realistic statistical mechanical models admit no analytical.
"The Yang-Baxter equation is a simple equation that can be represented by a picture that a two-year-old can draw," says Robert Weston of Heriot-Watt University in Edinburgh, UK.
Like the Euler. In the fields of statistical mechanics, knot theory, braid groups, and quantum theory, the Yang–Baxter equation has been a hot research topic, but in matrix theory, this special quadratic matrix equation has not been systematically studied yet. One reason is the fact that finding all the solutions is a difficult by: Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics Giuseppe Mussardo 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.
Igor Krichever. Professor, Director of Skoltech Center for Advanced Studies Statistical models, Yang-Baxter equation and related topics, and Symmetry, statistical mechanical models and applications (Tianjin, ) World Sci.
Publ., River Edge, NJ (), – (with O. .This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process.
The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics.For some recent development of solving the original Yang–Baxter equation or modern quantum Yang–Baxter equation, we refer the books.
The Yang–Baxter-like matrix equation has two trivial solutions X = 0 and X = A, but finding nontrivial solutions of (1) is not easy for an arbitrary matrix A since it is equivalent to solving a general Cited by: