The magnetization at high temperature for a $p$-spin interaction model with external field
Volume 34 / 2007
Applicationes Mathematicae 34 (2007), 97-111
MSC: 82D30, 60G15, 60G60.
DOI: 10.4064/am34-1-8
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 $\langle \sigma_i \rangle$ (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that $\langle \sigma_1 \rangle,\dots,\langle \sigma_n \rangle$ are asymptotically independent.
