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Gibbs Measures and Phase Transitions

E-BookPDFDRM AdobeE-Book
556 Seiten
Englisch
De Gruytererschienen am31.05.20112nd ext. ed

From a review of the first edition: 'This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] 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.' (F. Papangelou, Zentralblatt MATH)

The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.


Hans-Otto Georgii, Ludwig-Maximilians-Universität Munich, Germany.mehr
Verfügbare Formate
BuchGebunden
EUR194,95
E-BookPDFDRM AdobeE-Book
EUR210,00

Produkt

Klappentext
From a review of the first edition: 'This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] 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.' (F. Papangelou, Zentralblatt MATH)

The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.


Hans-Otto Georgii, Ludwig-Maximilians-Universität Munich, Germany.
Details
Weitere ISBN/GTIN9783110250329
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format HinweisDRM Adobe
FormatE107
Erscheinungsjahr2011
Erscheinungsdatum31.05.2011
Auflage2nd ext. ed
ReiheDe Gruyter Studies in Mathematics
Reihen-Nr.9
Seiten556 Seiten
SpracheEnglisch
Artikel-Nr.1031211
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1;Preface;8
2;Contents;12
3;Introduction;16
4;Part I General theory and basic examples;24
4.1;Chapter 1 Specifications of random fields;26
4.2;Chapter 2 Gibbsian specifications;40
4.3;Chapter 3 Finite state Markov chains as Gibbs measures;59
4.4;Chapter 4 The existence problem;72
4.5;Chapter 5 Specifications with symmetries;96
4.6;Chapter 6 Three examples of symmetry breaking;109
4.7;Chapter 7 Extreme Gibbs measures;129
4.8;Chapter 8 Uniqueness;155
4.9;Chapter 9 Absence of symmetry breaking. Non- existence;183
5;Part II Markov chains and Gauss fields as Gibbs measures;204
5.1;Chapter 10 Markov fields on the integers I;205
5.2;Chapter 11 Markov fields on the integers II;224
5.3;Chapter 12 Markov fields on trees;253
5.4;Chapter 13 Gaussian fields;271
6;Part III Shift- invariant Gibbs measures;304
6.1;Chapter 14 Ergodicity;305
6.2;Chapter 15 The specific free energy and its minimization;323
6.3;Chapter 16 Convex geometry and the phase diagram;353
7;Part IV Phase transitions in reflection positive models;380
7.1;Chapter 17 Reflection positivity;382
7.2;Chapter 18 Low energy oceans and discrete symmetry breaking;397
7.3;Chapter 19 Phase transitions without symmetry breaking;423
7.4;Chapter 20 Continuous symmetry breaking in N- vector models;448
8;Bibliographical Notes;468
9;References;510
10;List of Symbols;554
11;Index;556mehr
Kritik
"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."Fredos Papangelou, Zentralblatt MATHmehr