Eur. Phys. J. B 74, 139-149 (2010)
https://doi.org/10.1140/epjb/e2010-00022-9

Low temperature spin glass fluctuations: expanding around a spherical approximation

¹ Dipartimento di Fisica, Università di Roma La Sapienza and SMC, P.le Aldo Moro 2, 00185 Roma, Italy
² Institut de Physique Théorique, CEA - Saclay - Orme des Merisiers, 91191 Gif-sur-Yvette, France

Corresponding author: andrea.crisanti@phys.uniroma1.it

Received: 14 September 2009
Revised: 6 November 2009
Published online: 21 January 2010

Abstract

The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter Q(x) and, at the same time, keep track of Q_ab, its matrix aspect, and hence of the Hessian controlling stability, we investigate an expansion of the replicated free energy functional around its “spherical” approximation. This expansion is obtained by introducing a constraint-field and a (double) Legendre Transform expressed in terms of spin correlators and constraint-field correlators. The spherical approximation has the spin fluctuations treated with a global constraint and the expansion of the Legendre Transformed functional brings them closer and closer to the Ising local constraint. In this paper we examine the first contribution of the systematic corrections to the spherical starting point.