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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， 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

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