Published by De Gruyter 2011

Gibbs Measures and Phase Transitions

Hans-Otto Georgii

Volume 9 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110250329

Overview
Contents

About this book

A work of outstanding scholarship
Covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics
Informs about the state of the art in several directions
Accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability
Does not assume any prior knowledge of statistical mechanics

Author / Editor information

Hans-Otto Georgii, Ludwig-Maximilians-Universität Munich, Germany.

Reviews

"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Zentralblatt für Mathematik (review of the first edition)

"The book is an excellent basis for a serious study. It is carefully written, the proofs are detailed and clear, the examples are illuminating. Over 650 annotated references provide a useful orientation in the huge existing literature." Mathematical Reviews

Supplementary Materials

Contents

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Preface Requires Authentication Unlicensed Licensed Download PDF	VII
Contents Requires Authentication Unlicensed Licensed Download PDF	XI
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I. General theory and basic examples
Chapter 1 Specifications of random fields Requires Authentication Unlicensed Licensed Download PDF	9
Chapter 2 Gibbsian specifications Requires Authentication Unlicensed Licensed Download PDF	25
Chapter 3 Finite state Markov chains as Gibbs measures Requires Authentication Unlicensed Licensed Download PDF	44
Chapter 4 The existence problem Requires Authentication Unlicensed Licensed Download PDF	57
Chapter 5 Specifications with symmetries Requires Authentication Unlicensed Licensed Download PDF	81
Chapter 6 Three examples of symmetry breaking Requires Authentication Unlicensed Licensed Download PDF	94
Chapter 7 Extreme Gibbs measures Requires Authentication Unlicensed Licensed Download PDF	114
Chapter 8 Uniqueness Requires Authentication Unlicensed Licensed Download PDF	140
Chapter 9 Absence of symmetry breaking. Non-existence Requires Authentication Unlicensed Licensed Download PDF	168
Part II. Markov chains and Gauss fields as Gibbs measures
Chapter 10 Markov fields on the integers I Requires Authentication Unlicensed Licensed Download PDF	189
Chapter 11 Markov fields on the integers II Requires Authentication Unlicensed Licensed Download PDF	209
Chapter 12 Markov fields on trees Requires Authentication Unlicensed Licensed Download PDF	238
Chapter 13 Gaussian fields Requires Authentication Unlicensed Licensed Download PDF	256
Part III. Shift-invariant Gibbs measures
Chapter 14 Ergodicity Requires Authentication Unlicensed Licensed Download PDF	289
Chapter 15 The specific free energy and its minimization Requires Authentication Unlicensed Licensed Download PDF	308
Chapter 16 Convex geometry and the phase diagram Requires Authentication Unlicensed Licensed Download PDF	338
Part IV. Phase transitions in reflection positive models
Chapter 17 Reflection positivity Requires Authentication Unlicensed Licensed Download PDF	365
Chapter 18 Low energy oceans and discrete symmetry breaking Requires Authentication Unlicensed Licensed Download PDF	382
Chapter 19 Phase transitions without symmetry breaking Requires Authentication Unlicensed Licensed Download PDF	408
Chapter 20 Continuous symmetry breaking in N-vector models Requires Authentication Unlicensed Licensed Download PDF	433
Bibliographical Notes Requires Authentication Unlicensed Licensed Download PDF	453
Further Progress Requires Authentication Unlicensed Licensed Download PDF	489
References Requires Authentication Unlicensed Licensed Download PDF	495
References to the Second Edition Requires Authentication Unlicensed Licensed Download PDF	532
List of Symbols Requires Authentication Unlicensed Licensed Download PDF	539
Index Requires Authentication Unlicensed Licensed Download PDF	541

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd ext. ed.
Audience: Researchers, Graduate Students; Academic Libraries
Pages
- Front matter: 14
- Main content: 542
Keywords: Phase Transition; Statistical Mechanics; Gibbs Measures; Markov Chains; Gaussian Fields

eBook

Published: May 31, 2011
ISBN: 9783110250329

Hardcover

Published: May 17, 2011
ISBN: 9783110250299