The magnetization at high temperature for a p-spin interaction model with external field

Abstract

This paper is devoted to a detailed and rigorous study of the magnetization at high temperature for a p-spin interaction model with external field, generalizing the Sherrington-Kirkpatrick model. In particular, we prove that σ i (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that σ 1 , . . . , σ n are asymptotically independent.2000 Mathematics Subject Classification: 82D30, 60G15, 60G60.