Rigorous results on some simple spin glass models

Details Rigorous results on some simple spin glass models Rigorous results on some simple spin glass models

2002-06-28

arxiv.org/abs/cond-mat/0206562v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

33pp. Talk presented at Journees de Physique Statistique, Cergy, 2002

Scientific paper

In this paper we review some recent rigorous results that provide an essentially complete solution of a class of spin glass models introduced by Derrida in the 1980ies. These models are based on Gaussian random processes on $\{-1,1\}^N$ whose covariance is a function of a ultrametric distance on that set. We prove the convergence of the free energy as well as the Gibbs measures in an appropriate sense. These results confirm fully the predictions of the replica method including in situations where continuous replica symmetry breaking takes place.

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