Current Developments in Mathematics

Volume 2014

Introduction to the SK model

Pages: 231 – 291

DOI: http://dx.doi.org/10.4310/CDM.2014.v2014.n1.a4

Author

Dmitry Panchenko (Department of Mathematics, University of Toronto, Ontario, Canada)

Abstract

This paper is an overview of recent advances in spin glass models. Main focus is on the Sherrington–Kirkpatrick model and, in particular, on the results that explain the origin of various hypotheses at the centre of the well-established theory of spin glasses in physics, concerning the fine structure of the Gibbs measure.

Keywords

spin glasses, free energy, Parisi formula, ultrametricity

2010 Mathematics Subject Classification

60F10, 60G09, 60G15, 60K35, 82B44

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