Statistics Papers

Document Type

Technical Report

Date of this Version

1-2016

Publication Source

Journal of Statistical Physics

Volume

162

Issue

1

Start Page

63

Last Page

80

DOI

10.1007/s10955-015-1406-7

Abstract

We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian HN(σ) = σTJσ, where the coupling matrix J is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix J. As an application, we derive the limiting free energy of the random orthogonal model at high temperatures, which confirms non-rigorous calculations of Marinari et al. (J Phys A 27:7647, 1994). Our methods also apply to other well-known models of disordered systems, including the SK and Gaussian Hopfield models.

Copyright/Permission Statement

This is the pre-peer reviewed version of the following article: [Bhattacharya, B.B. & Sen, S. (2016). High Temperature Asymptotics of Orthogonal Mean-Filed Spin Glasses. Journal of Statistical Physics 162, no. 1: pp. 63-80], which has been published in final form at http://dx.doi.org/10.1007/s10955-015-1406-7. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

Keywords

large deviations, random orthogonal matrices, spherical integrals, spin glasses

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Date Posted: 25 October 2018

This document has been peer reviewed.