Abstract

Within the replica approach to mean-field spin glasses the transition from ergodichigh-temperature behaviour to the glassy low-temperature phase is marked bythe instability of the replica-symmetric saddle point. For general spin-glassmodels with non-Gaussian field distributions the corresponding Hessian is a2n × 2n matrix withthe number n of replicas tending to zero eventually. We block-diagonalize this Hessian matrix usingrepresentation theory of the permutation group and identify the blocks related to thespin-glass susceptibility. Taking the limit within these blocks we derive expressions for the de Almeida–Thouless line ofgeneral spin-glass models. Making these expressions specific to the cases of theSherrington–Kirkpatrick, Viana–Bray, and Lévy spin glasses, we obtain results in agreementwith previous findings using the cavity approach.

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