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Statistical Mechanics Of Lattice Systems


Statistical Mechanics Of Lattice Systems
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Statistical Mechanics Of Lattice Systems


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.



Equilibrium Statistical Mechanics Of Lattice Models


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


Statistical Mechanics Of Lattice Systems
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Author : David Lavis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Statistical Mechanics Of Lattice Systems written by David Lavis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.


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 multi particle 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 2) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this 1 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 include some of our discussion of exact results in this volume and some in Volume 2. The other main area of discussion in this volume is mean-field theory leading to closed form approximations. Although this is known not to give reliable results close to a critical region, it often provides a good qualitative picture for phase dia grams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available.



The Statistical Mechanics Of Lattice Gases Volume I


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.



Statistical Mechanics Of Lattice Systems


Statistical Mechanics Of Lattice Systems
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Author : David Lavis
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-03-08

Statistical Mechanics Of Lattice Systems written by David Lavis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-08 with Science categories.


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.



Statistical Mechanics Of Lattice Systems


Statistical Mechanics Of Lattice Systems
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Author : David Lavis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Statistical Mechanics Of Lattice Systems written by David Lavis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.


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.



Statistical Mechanics Of Lattice Systems


Statistical Mechanics Of Lattice Systems
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Author : David Lavis
language : en
Publisher: Springer
Release Date : 2010-12-01

Statistical Mechanics Of Lattice Systems written by David Lavis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Science categories.


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.



Statistical Mechanics Of Disordered Systems


Statistical Mechanics Of Disordered Systems
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Author : Anton Bovier
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-08

Statistical Mechanics Of Disordered Systems written by Anton Bovier 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 2006-06-08 with Mathematics categories.


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Statistical Mechanics Of Lattice Systems


Statistical Mechanics Of Lattice Systems
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Author : David Anthony Lavis
language : en
Publisher:
Release Date : 1999

Statistical Mechanics Of Lattice Systems written by David Anthony Lavis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Lattice dynamics categories.




Statistical Mechanics


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.