Gibbs Measures and Phase Transitions

Table of Contents

• Frontmatter
• Introduction
• 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 A variational characterization of Gibbs measures
  • 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 Ν-vector models
• Bibliographical Notes
• References
• List of Symbols
• Index
• Backmatter