Spin Glasses: A Challenge for Mathematicians

Cavity and Mean Field Models

Paperback Engels 2010 9783642055683
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In the 1980s, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". This rigorous book introduces this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.

Specificaties

ISBN13:9783642055683
Taal:Engels
Bindwijze:paperback
Aantal pagina's:586
Uitgever:Springer Berlin Heidelberg

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Inhoudsopgave

<P>0. Introduction.- 1. A Toy Model, the REM.- 2. The Sherrington-Kirkpatrick Model.- 3. The Capacity of the Perceptron: The Ising Case.- 4. Capacity of the Perceptron: The Gaussian and the Spherical Case.- 5. The Hopfield Model.- 6. The p-Spin Interaction Model at Low Temperature.- 7. The Diluted SK Model and the K-Sat Problems.- 8. An Assignment Problem.- A. Appendix.- Elements of Probability Theory.- References.- Index.</P>

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        Spin Glasses: A Challenge for Mathematicians