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Birkhäuser

Spin Glasses: Statics and Dynamics

Summer School, Paris 2007

  • Conference proceedings
  • © 2009

Overview

Editors:
  1. Anne Boutet Monvel

    1. Institut de Mathématique de Jussieu, Université Paris Diderot Paris 7, Paris, France

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  2. Anton Bovier

    1. Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • Combination of introductory and advanced matter
  • Up-to-date presentation of various angles of the problem, by leading researchers in the field

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

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Table of contents (12 papers)

  1. Front Matter

    Pages i-xii
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  2. Mean Field

    1. Front Matter

      Pages 1-1
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    2. A Short Course on Mean Field Spin Glasses

      • Anton Bovier, Irina Kurkova
      Pages 3-44

    3. REM Universality for Random Hamiltonians

      • Gérard Ben Arous, Alexey Kuptsov
      Pages 45-84

    4. Another View on Aging in the REM

      • Jiří Černý
      Pages 85-101

    5. Spin Glass Identities and the Nishimori Line

      • Pierluigi Contucci, Cristian Giardinà, Hidetoshi Nishimori
      Pages 103-121

    6. Self-averaging Identities for Random Spin Systems

      • Luca De Sanctis, Silvio Franz
      Pages 123-142

    7. Chaos in Mean-field Spin-glass Models

      • Tommaso Rizzo
      Pages 143-157

    8. A non Gaussian Limit Law for the Covariances of Spins in a SK Model with an External Field

      • Albert Hanen
      Pages 159-176

    9. A Limit Theorem for Mean Magnetisation in the Sherrington-Kirkpatrick Model with an External Field

      • Albert Hanen
      Pages 177-201

  3. Non-mean Field

    1. Front Matter

      Pages 203-203
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    2. A Percolation-theoretic Approach to Spin Glass Phase Transitions

      • Jonathan Machta, Charles M. Newman, Daniel L. Stein
      Pages 205-223

    3. Fluctuations in Finite-dimensional Spin-glass Dynamics

      • Claudio Chamon, Leticia F. Cugliandolo
      Pages 225-231

  4. Disordered Pinning Models

    1. Front Matter

      Pages 233-233
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    2. Renewal Sequences, Disordered Potentials, and Pinning Phenomena

      • Giambattista Giacomin
      Pages 235-270

    3. A Smoothing Inequality for Hierarchical Pinning Models

      • Hubert Lacoin, Fabio Lucio Toninelli
      Pages 271-278
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Keywords

About this book

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.

Editors and Affiliations

  • Institut de Mathématique de Jussieu, Université Paris Diderot Paris 7, Paris, France

    Anne Boutet Monvel

  • Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany

    Anton Bovier

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