导语

  

内容提要

  

    乔治,H-O著的《吉布斯测度和相变(第2版)(英文版)》不仅仅是对吉布斯测度和相变的一个简单的介绍，其中还包括统计力学下相变中的数学理论和广泛而具有深度的讨论。本书主要包括四部分，第一部分是理论的基本理论；第二部分是对经典理论一系列结果的总结；第三部分是在Zd上的空间分布均匀的吉布斯测度；第四部分是基于Zd移位不变性模型的相位变化的存在性。读者对象：数学和理论物理领域的研究生和科研工作者。

Introduction
Part Ⅰ. General theory and basic examples
Chapter 1 Specifications of random fields
  1.1  Preliminaries
  1.2  Prescribing conditional probabilities
  1.3  A-specifications
Chapter 2 Gibbsian specifications
  2.1  Potentials
  2.2  Quasilocality
  2.3  Gibbs representation of pre-modifications
  2.4  Equivalence of potentials
Chapter 3 Finite state Markov chains as Gibbs measures
  3.1  Markov specifications on the integers
  3.2  The one-dimensional Ising model
  3.A Appendix. Positive matrices
Chapter 4 The existence problem
  4.1  Local convergence of random fields
  4.2  Existence of cluster points
  4.3  Continuity results
  4.4  Existence and topological properties of Gibbs measures
  4.A Appendix. Standard Borel spaces
Chapter 5 Specifications with symmetries
  5.1  Transformations of specifications
  5.2  Gibbs measures with symmetries
Chapter 6 Three examples of symmetry breaking
  6.1  Inhomogeneous Ising chains
  6.2  The Ising ferromagnet in two dimensions
  6.3  Shlosman's random staircases
Chapter 7 Extreme Gibbs measures
  7.1  Tail triviality and approximation
  7.2  Some applications
  7.3  Extreme decomposition
  7.4  Macroscopic equivalence of Gibbs simplices
Chapter 8 Uniqueness
  8.1  Dobrushin's condition of weak dependence
  8.2  Further consequences of Dobrushin's condition
  8.3  Uniqueness in one dimension
Chapter 9 Absence of symmetry breaking. Non-existence
  9.1  Discrete symmetries in one dimension
  9.2  Continuous symmetries in two dimensions
Part Ⅱ. Markov chains and Gauss fields as Gibbs measures
Chapter 10 Markov fields on the integers I
  10.1  Two-sided and one-sided Markov property
  10.2  Markov fields which are Markov chains
  10.3  Uniqueness of the shift-invariant Markov field
Chapter 11 Markov fields on the integers II
  11.1  Boundary laws, uniqueness, and non-existence
  11.2  The Spitzer-Cox example of phase transition
  11.3  Kalikow's example of phase transition
  11.4  Spitzer's example of totally broken shift-invariance
Chapter 12 Markov fields on trees
  12.1  Markov chains and boundary laws
  12.2  The Ising model on Cayley trees
Chapter 13 Gaussian fields
  13.1  Gauss fields as Gibbs measures
  13.2  Gibbs measures for Gaussian specifications
  13.3  The homogeneous case
  13.A Appendix. Some tools of Gaussian analysis
Part Ⅲ. Shift-invariant Gibbs measures
Chapter 14 Ergodicity
  14.1  Ergodic random fields
  14.2  Ergodic Gibbs measures
  14.A Appendix. The multidimensional ergodic theorem
Chapter 15 The specific free energy and its minimization
  I5.I Relative entropy
  15.2  Specific entropy
  15.3  Specific energy and free energy
  15.4  The variational principle
  15.5  Large deviations and equivalence of ensembles
Chapter 16 Convex geometry and the phase diagram
  16.1  The pressure and its tangent functionals
  16.2  A geometric view of Gibbs measures
  16.3  Phase transitions with prescribed order parameters
  16.4  Ubiquity of pure phases
Part Ⅳ. Phase transitions in reflection positive models
Chapter 17 Reflection positivity
  17.1  The chessboard estimate
  17.2  Gibbs distributions with periodic boundary condition
Chapter 18 Low energy oceans and discrete symmetry breaking
  18.1  Percolation of spin patterns
  18.2  Discrete symmetry breaking at low temperatures
  18.3  Examples
Chapter 19 Phase transitions without symmetry breaking
  19.1  Potentials with degenerated ground states, and perturbations thereof
  19.2  Exploiting Sperner's lemma
  19.3  Models with an entropy-energy conflict
  19.A Appendix. Sperner's lemma
Chapter 20 Continuous symmetry breaking in N-vector models
  20.1  Some preliminaries
  20.2  Spin wave analysis, and spontaneous magnetization
Bibliographical Notes
Further Progress
References
References to the Second Edition
List of Symbols
Index