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July 2000 Replica symmetry breaking and exponential inequalities for the Sherrington-Kirkpatrick model
Michel Talagrand
Ann. Probab. 28(3): 1018-1062 (July 2000). DOI: 10.1214/aop/1019160325

Abstract

We provide an extremely accurate picture of the Sherrington – Kirkpatrick model in three cases:for high temperature, for large external field and for any temperature greater than or equal to 1 and sufficiently small external field. We describe the system at the level of the central limit theorem, or as physicists would say, at the level of fuctuations around the mean field. We also obtain much more detailed information, in the form of exponential inequalities that express a uniform control over higher order moments.We give a complete, rigorous proof that at the generic point of the predicted low temperature region there is “replica symmetry breaking,” in the sense that the system is unstable with respect to an infinitesimal coupling between two replicas.

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Michel Talagrand. "Replica symmetry breaking and exponential inequalities for the Sherrington-Kirkpatrick model." Ann. Probab. 28 (3) 1018 - 1062, July 2000. https://doi.org/10.1214/aop/1019160325

Information

Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1034.82027
MathSciNet: MR1797303
Digital Object Identifier: 10.1214/aop/1019160325

Subjects:
Primary: 82D30
Secondary: 60G15 , 60G70

Keywords: Disorder , Mean field

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • July 2000
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