Gibbs Measures and Phase Transitions 2nd Edition by Hans Otto Georgii 9783110250329 3110250322

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Product details:

ISBN 10: 3110250322

ISBN 13: 9783110250329

Author: Hans Otto Georgii

“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

Table of contents:

Part I. General Theory and Basic Examples
Chapter 1: Specifications of Random Fields
Chapter 2: Gibbsian Specifications
Chapter 3: Finite State Markov Chains as Gibbs Measures
Chapter 4: The Existence Problem
Chapter 5: Specifications with Symmetries
Chapter 6: Three Examples of Symmetry Breaking
Chapter 7: Extreme Gibbs Measures
Chapter 8: Uniqueness
Chapter 9: Absence of Symmetry Breaking. Non-Existence

Part II. Markov Chains and Gauss Fields as Gibbs Measures
Chapter 10: Markov Fields on the Integers I
Chapter 11: Markov Fields on the Integers II
Chapter 12: Markov Fields on Trees
Chapter 13: Gaussian Fields

Part III. Shift-Invariant Gibbs Measures
Chapter 14: Ergodicity
Chapter 15: The Specific Free Energy and Its Minimization
Chapter 16: Convex Geometry and the Phase Diagram

Part IV. Phase Transitions in Reflection Positive Models
Chapter 17: Reflection Positivity
Chapter 18: Low Energy Oceans and Discrete Symmetry Breaking
Chapter 19: Phase Transitions without Symmetry Breaking
Chapter 20: Continuous Symmetry Breaking in N-Vector Models

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Tags: Hans Otto Georgii, Gibbs, Measures, Transitions