2005/12/31 by V. Janiš, V. Janis, A. Klic +1 · 10 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete symmetry #Geometry #Homogeneous space #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Replica #Replica trick #Scheme (mathematics) #Spin glass #Statistical physics #Stochastic processes and statistical mechanics #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.74.054410
published in Physical Review B 74(5) (American Physical Society) · REVTeX4, 11 pages, no figures
openalex publication_date 2006/08/08 · arxiv created 2006/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 finitely many hierarchies are unstable and only the scheme with infinitely 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 number of hierarchies.