Spin Glasses: A Challenge for Mathematicians

Cavity and Mean Field Models
1. Auflage. Softcover version of original hardcover Auflage 2003
ISBN: 978-3-642-05568-3
Verlag: Springer

Buch, Englisch, 586 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 896 g

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science).

This book introduces in a rigorous manner 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.

Zielgruppe

Research

Autoren/Hrsg.

Talagrand, Michel

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Elektromagnetismus Magnetismus

Inhaltsverzeichnis

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.