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 Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie–Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin–Wagner and Lee–Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov–Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.
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 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 Systems written by David Anthony Lavis and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2013-06-29 with total page 437 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 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
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 of Lattice Systems written by David A. Lavis and published by Springer Science & Business Media. This book was released on 1999-03-08 with total page 394 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 the reader to the main areas in statistical mechanics and the theory of phase transitions. The development is built 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. Volume 2 includes extensive treatments of scaling theory, algebraic and real-space renormalization methods and the eight-vertex model. It also includes an account of series methods and a treatment of dimer assemblies.
Download or read book The Statistical Mechanics of Quantum Lattice Systems written by and published by European Mathematical Society. This book was released on 2009 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics.
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 Statistical mechanics of lattice systems written by David A. Lavis and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Statistical Mechanics of Lattice Gases written by Barry Simon and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Mechanics of Driven Diffusive Systems written by and published by Elsevier. This book was released on 1995-07-24 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension.Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail.Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these systems, the driven lattice gas was introduced roughly a decade ago. Since then, a number of surprising phenomena have been discovered including singular correlations at generic temperatures, as well as novel phase transitions, universality classes, and interfacial instabilities. This book summarizes current knowledge on driven systems, from apedagogical discussion of the original driven lattice gas to a brief survey of related models. Given that the topic is far from closed, much emphasis is placed on detailing open questions and unsolved problems as an incentive for the reader to pursue thesubject further.Provides a summary of current knowledge on driven diffusive systemsEmphasis is placed on detailing open questions and unsolved problemsCovers the entire subject from original driven lattice gas to a survey of related models
Download or read book Statistical Mechanics written by R.K. Pathria and published by Elsevier. This book was released on 2017-02-21 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.
Download or read book Convexity in the Theory of Lattice Gases written by Robert B. Israel and published by Princeton University Press. This book was released on 2015-03-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. 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.
