Exponential Control of Overlap in the Replica Method for p-Spin Sherrington-Kirkpatrick Model

2007/01/30 by Dmitry Panchenko
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B44

paper · pdf · doi:10.1007/s10955-007-9463-1

published as Journal of Statistical Physics, 2008, Vol. 130, No. 5, 831-842.

arxiv created 2007/01/30 · openalex publication_date 2007/11/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

Recently, Michel Talagrand computed the large deviations limit lim_N→∞(Na)^-1log \e Z_N^a for the moments of the partition function Z_N in the Sherrington-Kirkpatrick model for all real a≥ 0. For a≥ 1 the limit is given by Guerra's inverse bound and this result extends the classical physicist's replica method that corresponds to integer a. We give a new proof for a≥ 1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap.

Citations

• General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
• The replica method and solvable spin glass model
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model