Statistical Physics of Spin Glasses and Information Processing An Introduction [Paperback]

The present book provides the reader with a general perspective of an interdisciplinary field between statistical physics and information sciences/engineering. It is virtually the only book on the subject, except for a collection of papers published fourteen years ago. The field is expanding quite rapidly, and this self-contained presentation may be expected to acquire a wide audience in physics and engineering.

1. Mean-field theory of phase transitions
1.1. Ising model
1.2. Order parameter and phase transition
1.3. Mean-field theory
1.4. Infinite-range model
1.5. Variational approach
2. Mean-field theory of spin glasses
2.1. Spin glass and the Edwards-Anderson model
2.2. Sherrington-Kirkpatrick model
2.3. Replica-symmetric solution
3. Replica symmetry breaking
3.1. Stability of replica-symmetric solution
3.2. Replica symmetry breaking
3.3. Full RSB solution
3.4. Physical significance of RSB
3.5. TAP equation
4. Gauge theory of spin glasses
4.1. Phase diagram of finite-dimensional systems
4.2. Gauge transformation
4.3. Exact solution for the internal energy
4.4. Bound on the specific heat
4.5. Bound on the free energy and internal energy
4.6. Correlation functions
4.7. Entropy of frustration
4.8. Modified+-Jmodel
4.9. Gauge glass
4.10. Dynamical correlation function
5. Error-correcting codes
5.1. Error-correcting codes
5.2. Spin glass representation
5.3. Overlap
5.4. Infinite-range model
5.5. Replica symmetry breaking
5.6. Codes with finite connectivity
5.7. Convolutional code
5.8. Turbo code
5.9. CDMA multiuser demodulator
6. Image restoration
6.1. Stochastic approach to image restoration
6.2. Infinite-range model
6.3. Simulation
6.4. Mean-field annealing
6.5. Edges
6.6. Parameter estimation
7. Associative memory
7.1. Associative memory
7.2. Embedding a finite number of patterns
7.3. Many patterns embedded
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