Title: Stability of the replica-symmetric saddle point in general mean-field spin-glass models
Abstract:Within the replica approach to mean-field spin glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric ...Within the replica approach to mean-field spin glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle point. For general spin-glass models with non-Gaussian field distributions the corresponding Hessian is a 2n × 2n matrix with the number n of replicas tending to zero eventually. We block-diagonalize this Hessian matrix using representation theory of the permutation group and identify the blocks related to the spin-glass susceptibility. Taking the limit within these blocks we derive expressions for the de Almeida–Thouless line of general spin-glass models. Making these expressions specific to the cases of the Sherrington–Kirkpatrick, Viana–Bray, and Lévy spin glasses, we obtain results in agreement with previous findings using the cavity approach.Read More