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 $\left\langle\sigma_i\right\rangle$ (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that $\left\langle\sigma_1\right\rangle, \ldots,\left\langle\sigma_n\right\rangle$ are asymptotically independent.