Mean Field Models for Spin Glasses

This rigorous introduction to an exciting new research domain is aimed at the mathematically minded and requires no knowledge of any physics. In a new and reworked edition, this first volume presents six fundamental models and the techniques to study them.

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.

Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumes. Will bring a reader with no previous knowledge of Spin Glasses to the frontier of current research. The only fully rigorous treatise of this scale on the subject. This first volume presents the basic results and methods. Includes supplementary material: sn.pub/extras

Autorentext
M. Talagrand is Research Director in CNRS, and Member of the French Academy of Sciences since 2004.

Inhalt
Introduction.- 1. The Sherrington-Kirkpatrick Model.- 2. The Perceptron Model.- 3. The Shcherbina and Tirozzi Model.- 4. The Hopfield Model.- 5. The V-statistics Model.- 6. The Diluted SK Model and the K-Sat Problem.- 7. An Assignment Problem.- A. Appendix: Elements of Probability Theory.- References.- Index.- Glossary.