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

Volume 34 / 2007

David Márquez-Carreras 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.

Authors

  • David Márquez-CarrerasFacultat de Matemàtiques
    Universitat de Barcelona
    Gran Via 585, 08007 Barcelona, Spain
    e-mail

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