Potts Models And Related Problems In Statistical Mechanics
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Potts Models And Related Problems In Statistical Mechanics
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Author : Paul Purdon Martin
language : en
Publisher: World Scientific
Release Date : 1991
Potts Models And Related Problems In Statistical Mechanics written by Paul Purdon Martin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
Potts Models and Related Problems in Statistical Mechanics
Exactly Solved Models A Journey In Statistical Mechanics Selected Papers With Commentaries 1963 2008
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Author : Fa Yueh Wu
language : en
Publisher: World Scientific
Release Date : 2009-03-03
Exactly Solved Models A Journey In Statistical Mechanics Selected Papers With Commentaries 1963 2008 written by Fa Yueh Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-03 with Science categories.
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.
Exactly Soluble Models In Statistical Mechanics Historical Perspectives And Current Status
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Author : Christopher King
language : en
Publisher: World Scientific
Release Date : 1997-02-26
Exactly Soluble Models In Statistical Mechanics Historical Perspectives And Current Status written by Christopher King and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-26 with categories.
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).
Equilibrium Statistical Mechanics Of Lattice Models
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Author : David A. Lavis
language : en
Publisher: Springer
Release Date : 2015-01-31
Equilibrium Statistical Mechanics Of Lattice Models written by David A. Lavis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Science categories.
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.
Statistical Mechanics Made Simple A Guide For Students And Researchers
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Author : Daniel C Mattis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-04-08
Statistical Mechanics Made Simple A Guide For Students And Researchers written by Daniel C Mattis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-08 with categories.
This book is an elaboration of the author's lecture notes in a graduate course in statistical physics and thermodynamics, augmented by some material suitable for self-teaching as well as for undergraduate study. The first 4 or 5 chapters are suitable for an undergraduate course for engineers and physicists in Thermodynamics and Statistical Physics and include detailed study of the various ensembles and their connections to applied thermodynamics. The Debye law of specific heats and reasons for deviations from the Debye formulas are covered, as are the Einstein theories of Brownian motion, black-body radiation and specific heat of solids. Van der Waals gases and the reason for the apparent failure of his Law of Corresponding States are discussed.The last 5 chapters treat topics of recent interest to researchers, including: the Ising and Potts models, spin waves in ferromagnetic and anti-ferromagnetic media, sound propagation in non-ideal gases and the decay of sound waves, introduction to the understanding of glasses and spin glasses, superfluidity and superconductivity.The selection of material is wide-ranging and the mathematics for handling it completely self-contained, ranging from counting (probability theory) to quantum field theory as used in the study of fermions, bosons and as an adjunct in the solutions of the equations of classical diffusion-reaction theory. In addition to the standard material found in most recent books on statistical physics the constellation of topics covered in this text includes numerous original items:• Generalization of “negative temperature” to interacting spins• Derivation of Gibbs' factor from first principles• Exact free energy of interacting particles in 1D (e.g., classical and quantum Tonk's gas)• Introduction to virial expansions, Equations of State, Correlation Functions and “critical exponents”• Superfluidity in ideal and non-ideal fluids (both Bogolubov and Feynman theories)• Superconductivity: thermodynamical approach and the BCS theory• Derivation of “Central Limit Theorem” and its applications• Boltzmann's “H-Theorem” and the nonlinear Boltzmann equation• Exact solution of nonlinear Boltzmann Equation for electrons in time-dependent electric field and the derivation of Joule heating, transport parameters in crossed electric and magnetic fields, etc.• Frequency spectrum and decay of sound waves in gases• Exact evaluation of free energy and thermodynamic properties of the two-dimensional Ising model in regular and fully frustrated (spin-glass like) lattices• The “zipper” model of crystal fracture or polymer coagulation — calculation of Tc• Potts model in 2D: duality and Tc• “Doi's theory” of diffusion-limited chemical reactions with some exact results — including the evaluation of statistical fluctuations in radioactive decay• Thermodynamic Green Functions and their applications to fermions and bosons with an example drawn from random matrix theory and much more.
Gibbs Measures In Biology And Physics The Potts Model
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Author : Utkir A Rozikov
language : en
Publisher: World Scientific
Release Date : 2022-07-28
Gibbs Measures In Biology And Physics The Potts Model written by Utkir A Rozikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-28 with Mathematics categories.
This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Exactly Solved Models In Statistical Mechanics
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Author : Rodney J. Baxter
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Exactly Solved Models In Statistical Mechanics written by Rodney J. Baxter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Science categories.
Exploration of two-dimensional lattice models examines basic statistical mechanics, Ising models, spherical models, ice-type models, corner transfer matrices, and elliptic functions. 1982 edition, with author's 2007 update on subsequent developments.
An Introduction To Stochastic Processes And Nonequilibrium Statistical Physics
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Author : Horacio Sergio Wio
language : en
Publisher: World Scientific
Release Date : 1994-02-07
An Introduction To Stochastic Processes And Nonequilibrium Statistical Physics written by Horacio Sergio Wio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-07 with Science categories.
The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool.
Statistical Mechanics Made Simple
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Author : Daniel Charles Mattis
language : en
Publisher: World Scientific
Release Date : 2008
Statistical Mechanics Made Simple written by Daniel Charles Mattis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This second edition extends and improves on the first, illustrating through myriad examples, the principles and logic used in extending the simple laws of idealised Newtonian physics and quantum physics into the real world of noise and thermal fluctuations.
Lattice Statistics And Mathematical Physics Festschrift Dedicated To Professor Fa Yueh Wu On The Occasion Of His 70th Birthday Proceedings Of Apctp Nankai Joint Symposium
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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 2002-11-06
Lattice Statistics And Mathematical Physics Festschrift Dedicated To Professor Fa Yueh Wu On The Occasion Of His 70th Birthday Proceedings Of Apctp Nankai Joint Symposium written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-06 with Science categories.
This book contains thirty-six short papers on recent progress in a variety of subjects in mathematical and theoretical physics, written for the proceedings of a symposium in honor of the seventieth birthday of Professor F Y Wu, held at the Nankai Institute of Mathematics, October 7-11, 2001. The collection of papers is aimed at researchers, including graduate students, with an interdisciplinary interest and gives a brief introduction to many of the topics of current interest. These include new results on exactly solvable models in statistical mechanics, integrable through the Yang-Baxter equations, quantum groups, fractional statistics, random matrices, index theorems on the lattice, combinatorics, and other related topics.