Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

Abstract

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.

arXiv commentREVTeX4, 11 pages, no figures

References in corpus (3)

• Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
• Free energy fluctuations in Ising spin glasses
• Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space

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• Mean-field solution of the Potts glass near the transition temperature to the ordered phase
• The Parisi formula completed
• Continuous RSB mean-field solution of the Potts glass
• Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick
• Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model
• Ergodicity breaking in frustrated disordered systems: Replicas in mean-field spin-glass models