The Sherrington-Kirkpatrick Model

  • Dmitry┬áPanchenko
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Dmitry Panchenko
    Pages 1-31
  3. Dmitry Panchenko
    Pages 33-77
  4. Dmitry Panchenko
    Pages 79-115
  5. Dmitry Panchenko
    Pages 117-135
  6. Back Matter
    Pages 137-156

About this book

Introduction

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.

Keywords

Aizenman-Sims-Starr scheme Aldous-Hoover representation Dovbysh-Sudakov representation Gaussian processes Ghirlanda-Guerra identities Guerra replica symmetry breaking Parisi ansatz Parisi formula Poisson processes Poisson-Dirichlet processes Ruelle probability cascades Sherrington-Kirkpatrick model Talagrand positivity principle exchangeability p-spin models replica symmetry breaking spin glass models ultrametricity

Authors and affiliations

  • Dmitry┬áPanchenko
    • 1
  1. 1., Department of MathematicsTexas A&M UniversityCollege StationUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6289-7
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6288-0
  • Online ISBN 978-1-4614-6289-7
  • Series Print ISSN 1439-7382