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.
Download or read book Statistical Mechanics of Lattice Systems written by David Lavis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces readers to the main topics and the theory of phase transitions, building on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods.
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Download or read book Statistical Mechanics of Lattice Systems written by David Lavis and published by Springer Science & Business Media. This book was released on 1999-03-08 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.
Download or read book Statistical Mechanics of Lattice Models written by George Macdonald Bell and published by Ellis Horwood. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Disorder and Competition in Soluble Lattice Models written by Walter F. Wreszinski and published by World Scientific. This book was released on 1993 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: At present, existing literature on this subject matter can only be said to relate in minor areas to this work. Important concepts in statistical mechanics, such as frustration, localization, Lifshitz and Griffiths singularities, multicritical points, modulated phases, superselection sectors, spontaneous symmetry breaking and the Haldane phase, strange attractors and the Hausdorff dimension, and many others, are illustrated by exactly soluble lattice models. There are examples of simple lattice models which are shown to give rise to spectacular phase diagrams, with multicritical points and sequences of modulated phases. The models are chosen to enable a concise exposition as well as a connection with real physical systems (as dilute antiferromagnets, spin glasses and modulated magnets). A brief introduction to the properties of dynamical systems, an overview of conformal invariance and the Bethe Ansatz and a discussion of some general methods of statistical mechanics related to spontaneous symmetry breaking, are included in the appendices. A number of exercises are included in the text to help the comprehension of the most representative issues.
Download or read book Equilibrium Statistical Physics written by Michael Plischke and published by World Scientific. This book was released on 2006 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition of one of the most important and best selling textbooks in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.The discussion of strongly interacting condensed matter systems has been expanded. A chapter on stochastic processes has also been added with emphasis on applications of the Fokker-Planck equation.The modern theory of phase transitions occupies a central place. The chapter devoted to the renormalization group approach is largely rewritten and includes a detailed discussion of the basic concepts and examples of both exact and approximate calculations. The development of the basic tools includes a chapter on computer simulations in which both Monte Carlo method and molecular dynamics are introduced, and a section on Brownian dynamics added.The theories are applied to a number of important systems such as liquids, liquid crystals, polymers, membranes, Bose condensation, superfluidity and superconductivity. There is also an extensive treatment of interacting Fermi and Bose systems, percolation theory and disordered systems in general.
Download or read book Statistical Mechanics of Lattice Systems written by David Lavis and published by Springer. This book was released on 2010-12-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.
Download or read book Statistical Mechanics written by Teunis C Dorlas and published by CRC Press. This book was released on 2021-04-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Mechanics: Fundamentals and Model Solutions, Second Edition Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics. Features Updated throughout with new content from the field An established and well-loved textbook Contains new problems and solutions for further learning opportunity Author Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.
Download or read book Equilibrium Statistical Mechanics written by Gene Mazenko and published by Wiley-VCH. This book was released on 2000-10-10 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: A completely modern approach to statistical mechanics Gene Mazenko presents an introduction to statistical mechanics from the modern condensed matter physics point of view. Emphasizing symmetry principles, conservation laws, and the consequences of broken symmetry, all of which are crucial to a fundamental understanding of statistical physics, this volume discusses the role of broken translational symmetry in treating solids.Professor Mazenko develops a firm basis for the choice of macrovariables or thermodynamic variables, stressing the importance of Nambu-Goldstone modes. He develops this theory beyond the usual examples of simple fluids with discussions of magnets, superfluids, and solids. Based on the author's more than 30 years of experience with this subject, Equilibrium Statistical Mechanics: * Develops the structure of statistical mechanics and thermodynamics from fundamentals * Highlights the approach of coarse graining in statistical mechanics * Discusses ergodic theory and information theory * Treats phase transitions in a number of specific applications * Includes copious examples and end-of-chapter problems * Gives full development to the rich history of this topic Look for Mazenko's forthcoming volumes, Fluctuations, Order, and Defects; Nonequilibrium Statistical Mechanics; and Field Theory Methods in Statistical Mechanics. Combined with this self-contained volume, these works span the entire graduate-level program.
Download or read book Statistical Physics I written by M. Toda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of Statistical Physics is an introduction to the theories of equilibrium statistical mechanics, whereas the second volume (Springer Ser. Solid-State Sci., Vol. 31) is devoted to non equilibrium theories. Particular emphasis is placed on fundamental principles and basic con cepts and ideas. We start with physical examples of probability and kinetics, and then describe the general principles of statistical mechanics, with appli cations to quantum statistics, imperfect gases, electrolytes, and phase tran sitions, including critical phenomena. Finally, ergodic problems, the me chanical basis of statistical mechanics, are presented. The original text was written in Japanese as a volume of the Iwanami Series in Fundamental Physics, supervised by Professor H. Yukawa. The first edition was published in 1973 and the second in 1978. The English edition has been divided into two volumes at the request of the publisher, and the chapter on ergodic problems, which was at the end of the original book, is included here as Chapter 5. Chapters 1,2,3 and part of Chapter 4 were written by M. Toda, and Chapters 4 and 5 by N. Saito. More extensive references have been added for further reading, and some parts of the final chapters have been revised to bring the text up to date. It is a pleasure to express my gratitude to Professor P. Fulde for his detailed improvements in the manuscript, and to Dr. H. Lotsch of Springer Verlag for his continued cooperation.
Download or read book Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter written by Alessandro Manacorda and published by Springer. This book was released on 2018-07-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2003-01-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Download or read book The Statistical Mechanics of Lattice Gases Volume I written by Barry Simon and published by Princeton University Press. This book was released on 2014-07-14 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of high and low temperature expansions. The second volume will deal with the Peierls construction, infrared bounds, Lee-Yang theorems, and correlation inequality. This comprehensive work will be a useful reference not only to scientists working in mathematical statistical mechanics but also to those in related disciplines such as probability theory, chemical physics, and quantum field theory. It can also serve as a textbook for advanced graduate students. Originally published in 1993. 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.
Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Courier Corporation. This book was released on 2013-07-02 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the solution of two-dimensional lattice models. Topics include basic statistical mechanics, Ising models, the mean field model, the spherical model, ice-type models, corner transfer matrices, hard hexagonal models, and elliptic functions. The author has updated the 1989 version with a new chapter, "Subsequent Developments," for the 2007 edition.
Download or read book Nonequilibrium Phase Transitions in Lattice Models written by Joaquin Marro and published by Cambridge University Press. This book was released on 1999-05-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.
Download or read book Classical Equilibrium Statistical Mechanics written by Colin J. Thompson and published by . This book was released on 1988 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive work provides a rigorous introduction to statistical mechanics, which aims to relate microscopic properties of matter to observed macroscopic, or bulk, behavior of physical systems. The foundations of statistical mechanics, laid down by Gibbs, are presented in detail along with an introductory chapter on thermodynamics. Other topics covered include model systems and the thermodynamic limit; theories of phase transitions; fluctuations and correlations; exactly solved models; scaling theory; and the renormalization group. An important feature of the book is many problems and worked solutions which provide a timely demonstration of current research activity in the field.
