Spin Glasses: Statics and Dynamics

Summer School, Paris 2007

  • Anne Boutet de Monvel
  • Anton Bovier

Part of the Progress in Probability book series (PRPR, volume 62)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Mean Field

    1. Front Matter
      Pages 1-1
    2. Anton Bovier, Irina Kurkova
      Pages 3-44
    3. Gérard Ben Arous, Alexey Kuptsov
      Pages 45-84
    4. Jiří Černý
      Pages 85-101
    5. Pierluigi Contucci, Cristian Giardinà, Hidetoshi Nishimori
      Pages 103-121
    6. Luca De Sanctis, Silvio Franz
      Pages 123-142
    7. Tommaso Rizzo
      Pages 143-157
  3. Non-mean Field

    1. Front Matter
      Pages 203-203
    2. Jonathan Machta, Charles M. Newman, Daniel L. Stein
      Pages 205-223
    3. Claudio Chamon, Leticia F. Cugliandolo
      Pages 225-231
  4. Disordered Pinning Models

    1. Front Matter
      Pages 233-233
    2. Hubert Lacoin, Fabio Lucio Toninelli
      Pages 271-278

About these proceedings

Introduction

Over the last decade, spin glass theory has turned from a fascinating part of t- oretical physics to a ?ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious “Parisi solution” of the Sherrington–Kirkpatrick mean ?eld model of spin glasses, due to the work of Guerra, Talagrand, and others. At the same time, new aspects and applications of the methods developed there have come up. The presentvolumecollects a number of reviewsaswellas shorterarticlesby lecturers at a summer school on spin glasses that was held in July 2007 in Paris. These articles range from pedagogical introductions to state of the art papers, covering the latest developments. In their whole, they give a nice overview on the current state of the ?eld from the mathematical side. The review by Bovier and Kurkova gives a concise introduction to mean ?eld models, starting with the Curie–Weiss model and moving over the Random Energymodels up to the Parisisolutionof the Sherrington–Kirkpatrikmodel. Ben Arous and Kuptsov present a more recent view and disordered systems through the so-called local energy statistics. They emphasize that there are many ways to look at Hamiltonians of disordered systems that make appear the Random Energy model (or independent random variables) as a universal mechanism for describing certain rare events. An important tool in the analysis of spin glasses are correlation identities.

Keywords

Potential STATISTICA Variance disordered systems spin glasses statistical mechanics thermodynamics

Editors and affiliations

  • Anne Boutet de Monvel
    • 1
  • Anton Bovier
    • 2
  1. 1.Institut de Mathématique de JussieuUniversité Paris Diderot Paris 7ParisFrance
  2. 2.Institut für Angewandte MathematikRheinische Friedrich-Wilhelms-UniversitätBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-9891-0
  • Copyright Information Birkhäuser Basel 2009
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8999-4
  • Online ISBN 978-3-7643-9891-0
  • About this book
Industry Sectors
Pharma
Biotechnology
Telecommunications
Consumer Packaged Goods
Aerospace
Oil, Gas & Geosciences