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Author : D. A. Dubin
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (45 download)
Download or read book Solvable Models in Algebraic Statistical Mechanics written by D. A. Dubin and published by . This book was released on 1974 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Purdon Martin
Publisher : World Scientific
ISBN 13 : 9814507164
Total Pages : 363 pages
Book Rating : 4.8/5 (145 download)
Download or read book Potts Models And Related Problems In Statistical Mechanics written by Paul Purdon Martin and published by World Scientific. This book was released on 1991-02-28 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:IntroductionTransfer Matrices: On Commuting Transfer MatricesOn Exactly Solved CasesAlgebra: General PrinciplesTemperley-Lieb Algebra: Generic CasesSpecial CasesGraph Temperley-Lieb AlgebrasHecke AlgebrasAlgebraic Formalism for ZQ SymmetryThe Modelling of Phase TransitionsVertex Models and Related Algebras, Braids and Cables Readership: Mathematical physicists. Keywords:Yang-Baxter Algebras;Algebraic Methods of Statistical Mechanics;Potts Model;Transfer Matrices;Solvable Models;Temperly-Lieb Algebras;Hecke Algebras;Generalized Clifford Algebras;Representations;Partition Functions;Phase Transitions;Vertex Models;Braid GroupReview: “This is an excellent survey of the Potts model and related matters in statistical mechanics. The first chapter constitutes a good introduction to statistical mechanics with a discussion of modelling principles, partition functions and Hamiltonians, lattices, statistical mechanics functions such as free energy. There are good general discussions of phase transitions, order parameters and critical exponents. Then the Potts models are defined and related to dichromatic polynomials and to the special case of the Ising model. The chapter ends with a discussion of block spin renormalization … This book is a fine source of basic results about the Potts model and its mathematical physics environment.” Mathematical Reviews
Author : Michio Jimbo
Publisher : American Mathematical Soc.
ISBN 13 : 0821803204
Total Pages : 180 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Analysis of Solvable Lattice Models written by Michio Jimbo and published by American Mathematical Soc.. This book was released on 1995 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.
Author : Fa Yueh Wu
Publisher : World Scientific
ISBN 13 : 9812813896
Total Pages : 661 pages
Book Rating : 4.8/5 (128 download)
Download or read book Exactly Solved Models written by Fa Yueh Wu and published by World Scientific. This book was released on 2009 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume provides a comprehensive overview of exactly solved models in statistical mechanics by looking at the scientific achievements of F Y Wu in this and related fields, which span four decades of his career. The book is organized into topics ranging from lattice models in condensed matter physics to graph theory in mathematics, and includes the author's pioneering contributions. Through insightful commentaries, the author presents an overview of each of the topics and an insider's look at how crucial developments emerged. With the inclusion of important pedagogical review articles by the author, Exactly Solved Models is an indispensable learning tool for graduate students, and an essential reference and source book for researchers in physics and mathematics as well as historians of science.
Author : Rodney J. Baxter
Publisher : Elsevier
ISBN 13 : 1483265943
Total Pages : 499 pages
Book Rating : 4.4/5 (832 download)
Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Elsevier. This book was released on 2016-06-12 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly Solved Models in Statistical Mechanics
Author : Christopher King
Publisher : World Scientific
ISBN 13 : 9814546593
Total Pages : 234 pages
Book Rating : 4.8/5 (145 download)
Download or read book Exactly Soluble Models In Statistical Mechanics - Historical Perspectives And Current Status written by Christopher King and published by World Scientific. This book was released on 1997-02-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on 'Exactly Soluble Models in Statistical Mechanics: Historical Perspectives and Current Status', held at Northeastern University in March 1996 — the first ever conference to deal exclusively with this topic. Besides invited presentations by leading researchers in the field, the conference held a session of contributed papers by participants from throughout the world. The proceedings, which include both the invited and the contributed papers, reflect the broad range of interest in exactly soluble models as well as the diverse fields in physics and mathematics that they connect. Apart from providing concise and timely reviews, the papers in this volume give a snapshot of the current state of affairs. The topics covered range from a historical survey of the field (by E H Lieb) to the latest formulation of a star-star transformation of spin models (by R J Baxter).
Author : Vladislav Fridkin
Publisher :
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.:/5 (224 download)
Download or read book Reflection Equations in Exactly Solvable Models of Statistical Mechanics written by Vladislav Fridkin and published by . This book was released on 1999 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Barry M McCoy
Publisher : Oxford University Press, USA
ISBN 13 : 0199556636
Total Pages : 641 pages
Book Rating : 4.1/5 (995 download)
Download or read book Advanced Statistical Mechanics written by Barry M McCoy and published by Oxford University Press, USA. This book was released on 2010 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: McCoy presents the advances made in statistical mechanics over the last 50 years, including mathematical theorems on order and phase transitions, numerical and series computations of phase diagrams and solutions for important solvable models such as Ising and 8 vortex.
Author : Fa Yueh Wu
Publisher : World Scientific
ISBN 13 : 9814471224
Total Pages : 661 pages
Book Rating : 4.8/5 (144 download)
Download or read book Exactly Solved Models: A Journey In Statistical Mechanics - Selected Papers With Commentaries (1963–2008) written by Fa Yueh Wu and published by World Scientific. This book was released on 2009-03-03 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume provides a comprehensive overview of exactly solved models in statistical mechanics by looking at the scientific achievements of F Y Wu in this and related fields, which span four decades of his career. The book is organized into topics ranging from lattice models in condensed matter physics to graph theory in mathematics, and includes the author's pioneering contributions. Through insightful commentaries, the author presents an overview of each of the topics and an insider's look at how crucial developments emerged. With the inclusion of important pedagogical review articles by the author, Exactly Solved Models is an indispensable learning tool for graduate students, and an essential reference and source book for researchers in physics and mathematics as well as historians of science.
Author : Yupeng Wang
Publisher : Springer
ISBN 13 : 3662467569
Total Pages : 303 pages
Book Rating : 4.6/5 (624 download)
Download or read book Off-Diagonal Bethe Ansatz for Exactly Solvable Models written by Yupeng Wang and published by Springer. This book was released on 2015-04-21 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
Author : David A. Lavis
Publisher : Springer
ISBN 13 : 9401794308
Total Pages : 801 pages
Book Rating : 4.4/5 (17 download)
Download or read book Equilibrium Statistical Mechanics of Lattice Models written by David A. Lavis and published by Springer. This book was released on 2015-01-31 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef—Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Author : Colin J. Thompson
Publisher : Princeton University Press
ISBN 13 : 1400868688
Total Pages : 289 pages
Book Rating : 4.4/5 (8 download)
Download or read book Mathematical Statistical Mechanics written by Colin J. Thompson and published by Princeton University Press. This book was released on 2015-03-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Chin Kun Hu
Publisher : World Scientific
ISBN 13 : 9814644080
Total Pages : 418 pages
Book Rating : 4.8/5 (146 download)
Download or read book Progress In Statistical Mechanics - Proceedings Of The 1986 And 1988 Workshops written by Chin Kun Hu and published by World Scientific. This book was released on 1988-10-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Critical Phenomena, Field Theory and Renormalisation Group (T-M Yan & S C-C Lin)Field Theories of Surfaces and Interfaces (S C-C Lin)Spiral Self-Avoiding Walks (K Y Lin)Critical Phenomena on Fractal Lattices (Doochul Kim)Percolation and Phase Transitions: Towards a Unified Theory of Phase Transitions (C-K Hu)Real Space Approach to Disordered Systems (S-Y Wu)Three Routes to Chaos: Period Doubling, Intermittency and Quasiperiodicity (B Hu)Ordering Kinetics in Phase Transitions (K Kawasaki)A Design of Analog Circuit for Studies of Transitions to Chaos in a RF-Driven Josephson Junction (J C Huang et al)Potts Model and Graph Theory (F Y Wu)Number and Size of Convex Polygons on the Square Lattice (K Y Lin)Exactly Solvable Models in Statistical Mechanics and Automorphisms of Algebraic Varieties (J-M Maillard)The Application of the Transfer Matrix Method to the Phase Transition of Ising Model (T Oguchi et al)Coherent-Anomaly Method in Critical Phenomena (M Katori & M Suzuki)Monte Carlo Study of Percolation Transitions and Phase Transitions in Interacting Systems (C-K Hu & K-S Mak)Anisotropic Surface Tension and Equilibrium Crystal Shapes (R K P Zia)The Structure Making and Breaking Effects of Ion Solvation in Water (J-L Lin & C-Y Mou)Ordering Processes in Two-Dimensional Quantum Spin Systems (S=1/2) (S Miyashita)Phase Transitions in Arrays of Josephson Junctions (M Y Choi) Readership: Theoretical physicists and condensed matter physicists.
Author : Huzihiro Araki
Publisher : Springer Science & Business Media
ISBN 13 : 9401728232
Total Pages : 452 pages
Book Rating : 4.4/5 (17 download)
Download or read book Quantum and Non-Commutative Analysis written by Huzihiro Araki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
Author : Susan Montgomery
Publisher : American Mathematical Soc.
ISBN 13 : 0821807382
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)
Download or read book Hopf Algebras and Their Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1993-10-28 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Author : Chin-Kun Hu
Publisher : World Scientific
ISBN 13 : 9789971507145
Total Pages : 424 pages
Book Rating : 4.5/5 (71 download)
Download or read book Progress in Statistical Mechanics written by Chin-Kun Hu and published by World Scientific. This book was released on 1988 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anton Alekseev
Publisher : Springer Nature
ISBN 13 : 3030781488
Total Pages : 652 pages
Book Rating : 4.0/5 (37 download)
Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
