Equilibrium Statistical Mechanics Of Lattice Models
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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 Of Lattice Systems
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Author : Sacha Friedli
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-23
Statistical Mechanics Of Lattice Systems written by Sacha Friedli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Statistical Mechanics
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Author : Teunis C Dorlas
language : en
Publisher: CRC Press
Release Date : 2021-04-15
Statistical Mechanics written by Teunis C Dorlas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Science categories.
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.
Equilibrium Statistical Physics
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Author : Michael Plischke
language : en
Publisher: World Scientific
Release Date : 1994
Equilibrium Statistical Physics written by Michael Plischke 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 with Science categories.
This textbook concentrates on modern topics in statistical physics with an emphasis on strongly interacting condensed matter systems. The book is self-contained and is suitable for beginning graduate students in physics and materials science or undergraduates who have taken an introductory course in statistical mechanics. Phase transitions and critical phenomena are discussed in detail including mean field and Landau theories and the renormalization group approach. The theories are applied to a number of interesting systems such as magnets, liquid crystals, polymers, membranes, interacting Bose and Fermi fluids; disordered systems, percolation and spin of equilibrium concepts are also discussed. Computer simulations of condensed matter systems by Monte Carlo-based and molecular dynamics methods are treated.
The Statistical Mechanics Of Lattice Gases Volume I
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Author : Barry Simon
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
The Statistical Mechanics Of Lattice Gases Volume I written by Barry Simon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Science categories.
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.
Nonequilibrium Statistical Mechanics In One Dimension
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Author : Vladimir Privman
language : en
Publisher: Cambridge University Press
Release Date : 1997-02-20
Nonequilibrium Statistical Mechanics In One Dimension written by Vladimir Privman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-20 with Science categories.
Self-contained and up-to-date guide to one-dimensional reactions, dynamics, diffusion and adsorption.
Nonequilibrium Phase Transitions In Lattice Models
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Author : Joaquin Marro
language : en
Publisher: Cambridge University Press
Release Date : 2005-09-08
Nonequilibrium Phase Transitions In Lattice Models written by Joaquin Marro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-08 with Science categories.
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, examining simulation results in detail. Later chapters discuss absorbing-state transitions, and examine a variety of systems subject to dynamic disorder. The book discusses the effects of multiparticle rules, nonunique absorbing-states and conservation laws, as well as the use of methods such as mean-field theory, Monte Carlo simulation and the concept of universality. It also includes detailed references and examples using simple respresentations of nature to describe real systems.
Statistical Mechanics For Engineers
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Author : Isamu Kusaka
language : en
Publisher: Springer
Release Date : 2015-09-10
Statistical Mechanics For Engineers written by Isamu Kusaka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-10 with Science categories.
This book provides a gentle introduction to equilibrium statistical mechanics. The particular aim is to fill the needs of readers who wish to learn the subject without a solid background in classical and quantum mechanics. The approach is unique in that classical mechanical formulation takes center stage. The book will be of particular interest to advanced undergraduate and graduate students in engineering departments.
Statistical Mechanics
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Author : R. K. Pathria
language : en
Publisher: Elsevier
Release Date : 2016-06-30
Statistical Mechanics written by R. K. Pathria and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Technology & Engineering categories.
International Series in Natural Philosophy, Volume 45: Statistical Mechanics discusses topics relevant to explaining the physical properties of matter in bulk. The book is comprised of 13 chapters that primarily focus on the equilibrium states of physical systems. Chapter 1 discusses the statistical basis of thermodynamics, and Chapter 2 covers the elements of ensemble theory. Chapters 3 and 4 tackle the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 reviews the theory of simple gases. Chapters 7 and 8 discuss the ideal Bose and Fermi systems. The book also covers the cluster expansion, pseudopotential, and quantized field methods. The theory of phase transitions and fluctuations are then discussed. The text will be of great use to researchers who wants to utilize statistical mechanics in their work.
Convexity In The Theory Of Lattice Gases
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Author : Robert B. Israel
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Convexity In The Theory Of Lattice Gases written by Robert B. Israel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Science categories.
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.