The p-spin interaction model with external field

Xavier Bardina, David Màrquez-Carreras, Carles Rovira and Samy Tindel.

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain
Département de Mathématiques, Institut Galilée - Université Paris 13,  Avenue  J. B. Clément, 93430-Villetaneuse, France.

Abstract

This paper is dev

oted to a detailed study of a $p$-spins interaction model with external field, including some sharp bounds on the speed of self averaging of the  verlap as well as a central limit theorem for its fluctuations, the thermodynamical limit for the free energy and the definition of an Almeida-Thouless type line. Those  esults show that the external field dominates the tendency to disorder induced by the increasing level of interaction between spins, and our system will share many of  ts features with the SK model, which is certainly not the case when the external magnetic field vanishes.

Published in: Potential Analysis, 21 (4), 311-362, 2004