2003/12/31 by V. Janiš, V. Janis · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Discrete mathematics #Hierarchy #Homogeneity (statistics) #Material Dynamics and Properties #Mathematical physics #Mathematics #Metric space #Physics #Stability (learning theory) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Ultrametric space #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.71.214403
published as Phys. Rev. B71, 214403 (2005) · REVTeX4, 22 pages, second extended version to be published in Phys. Rev. B
arxiv created 2005/04/20 · openalex publication_date 2005/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.