【正版全新】吉布斯测度和相变 Hans-Otto Ge***ii著 世界图书出版公司北京公司 9787510054020 电子版 免费 pdf 下载 azw3 fb2 caj mobi

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Introduction

Part Ⅰ.General theory and basic examples

Chapter 1 Specificati*** of random fields

1.1 Preliminaries

1.2 Prescribing conditional probabilities

1.3 λ—specificati***

Chapter 2 Gibbsian specificati***

2.1 Potentials

2.2 Quasilocality

2.3 Gibbs representation of pre—modificati***

2.4 Equivalence of potentials

Chapter 3 Finite state Markov chains as Gibbs measures

3.1 Markov specificati*** on the integers

3.2 The one—dimensional Ising model

3.A Appendix.Positive matrices

Chapter 4 The estence problem

4.1 Local convergence of random fields

4.2 Estence of cluster points

4.3 Continuity results

4.4 Estence and topological properties of Gibbs measures

4.A Appendix.Standard Borel spaces

Chapter 5 Specificati*** with symmetries

5.1 Transformati*** of specificati***

5.2 Gibbs measures with symmetries

Chapter 6 Three examples of symmetry breaking

6.1 Inhomogeneous Ising chains

6.2 The Ising ferromag in two dimensi***

6.3 Shlosman's random staircases

Chapter 7 Extreme Gibbs measures

7.1 Tail triviality and appromation

7.2 Some applicati***

7.3 Extreme deposition

7.4 Macroscopic equivalence of Gibbs simplices

Chapter 8 Uniqueness

8.1 Dobrushin's condition of weak dependence

8.2 Further c***equences of Dobrushin's condition

8.3 Uniqueness in one dimension

Chapter 9 Absence of symmetry breaking.Non—estence

9.1 Discrete symmetries in one dimension

9.2 Continuous symmetries in two dimensi***

Part Ⅱ.Markuv 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 M arkov fields on the integers Ⅱ

11.1 Boundary laws， uniqueness， and non—estence

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 specificati***

13.3 The homogeneous case

13.A Appendix.Some tools of Gaussian ***ysis

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

I5.1 Relative entropy

15.2 Specific entropy

15.3 Specific energy and free energy

15.4 The variational principle

15.5 Large deviati*** 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 transiti*** with prescribed order parameters

1*** Ubiquity of pure phases

Part IV.Phase transiti*** in reflection positive models

Chapter 17 Reflection positivity

17.1 The chessboard estimate

17.2 Gibbs distributi*** with periodic boundary condition

Chapter 18 Low energy oceans and discrete symmetry breaki8.1 Percolation of spin patterns

18.2 Discrete symmetry breaking at low temperatures

18.3 Examples

Chapter 19 Phase transiti*** without symmetry breaking

19.1 Potentials with degenerated ground states， and perturbati*** 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 ***ysis， and spontaneous magization

Bibliographical Notes

Further Progress

References

References to the Second Edition

List of Symbols

Index

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