Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space

Abstract

We use real replicas within the Thouless, Anderson and Palmer construction to investigate stability of solutions with respect to uniform scalings in the phase space of the Sherrington-Kirkpatrick model. We show that the demand of homogeneity of thermodynamic potentials leads in a natural way to a thermodynamically dependent ultrametric hierarchy of order parameters. The derived hierarchical mean-field equations appear equivalent to the discrete Parisi RSB scheme. The number of hierarchical levels in the construction is fixed by the global thermodynamic homogeneity expressed as generalized de Almeida Thouless conditions. A physical interpretation of a hierarchical structure of the order parameters is gained.

arXiv commentREVTeX4, 22 pages, second extended version to be published in Phys. Rev. B

References in corpus (4)

• The structural glass transition and the entropy of the metastable states
• Thermodynamics of glasses: a first principle computation
• Modified TAP equations for the SK spin glass
• Replica trick with real replicas: A way to build in thermodynamic homogeneity

Cited by in corpus (9)

• Mean-field solution of the Potts glass near the transition temperature to the ordered phase
• Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature
• The Parisi formula completed
• Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick
• Continuous RSB mean-field solution of the Potts glass
• Incompleteness of the Thouless, Anderson, and Palmer mean-field description of the spin-glass phase
• Thermodynamic origin of order parameters in mean-field models of spin glasses
• 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