- Title Pages
- Preface
- 1 Introduction to information theory
- 2 Statistical physics and probability theory
- 3 Introduction to combinatorial optimization
- 4 A probabilistic toolbox
- 5 The random energy model
- 6 The random code ensemble
- 7 Number partitioning
- 8 Introduction to replica theory
- 9 Factor graphs and graph ensembles
- 10 Satisfiability
- 11 Low-density parity-check codes
- 12 Spin glasses
- 13 Bridges: Inference and the Monte Carlo method
- 14 Belief propogation
- 15 Decoding with belief propagation
- 16 The assignment problem
- 17 Ising models on random graph
- 18 Linear equations with Boolean variables
- 19 The 1RSB cavity method
- 20 Random K-satisfiability
- 21 Glassy states in coding theory
- 22 An ongoing story
- Appendix A Symbols and notation
- References
- Index

# The random energy model

# The random energy model

- Chapter:
- (p.93) 5 The random energy model
- Source:
- Information, Physics, and Computation
- Author(s):
### Marc Mézard

### Andrea Montanari

- Publisher:
- Oxford University Press

The random energy model is probably the simplest statistical physics model of a disordered system which exhibits a phase transition. This chapter studies its thermodynamic properties and its phase transition, and describes in detail the condensation phenomenon at work in the low temperature phase. The same mathematical structure and techniques appear in a large number of contexts. This is witnessed by the examples from information theory and combinatorial optimization presented in the next two chapters.

*Keywords:*
random energy model, phase transition, condensation, thermodynamic properties, low temperature phase

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- Title Pages
- Preface
- 1 Introduction to information theory
- 2 Statistical physics and probability theory
- 3 Introduction to combinatorial optimization
- 4 A probabilistic toolbox
- 5 The random energy model
- 6 The random code ensemble
- 7 Number partitioning
- 8 Introduction to replica theory
- 9 Factor graphs and graph ensembles
- 10 Satisfiability
- 11 Low-density parity-check codes
- 12 Spin glasses
- 13 Bridges: Inference and the Monte Carlo method
- 14 Belief propogation
- 15 Decoding with belief propagation
- 16 The assignment problem
- 17 Ising models on random graph
- 18 Linear equations with Boolean variables
- 19 The 1RSB cavity method
- 20 Random K-satisfiability
- 21 Glassy states in coding theory
- 22 An ongoing story
- Appendix A Symbols and notation
- References
- Index