This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.

Contents:

• Introduction
• Spin Glasses:
  • The Replica Approach
  • The TAP Approach
  • Breaking the Replica Symmetry
  • The Nature of the Spin Glass Phase
  • The Cavity Method
  • Dynamics
• Optimization:
  • Combinatorial Optimization Problems
  • Simulated Annealing
  • Analytical Results
• Biological Applications:
  • Prebiotic Evolution and Spin Glasses. Brain Modelling. The Hopfield Model and its Variations
• Reprints