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Journal Articles Journal of Statistical Physics Year : 2005

The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature

Abstract

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising and Sherrington-Kirpatrick temperatures are high enough, we prove that: (ii) the value of the pressure is given by a suitable replica symmetric solution, and (iii) the fluctuations of the pressure are of order of the inverse of the square of the volume with a normal distribution in the limit. In this regime, the pressure can be expressed in terms of random field Ising models.
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Dates and versions

hal-00003866 , version 1 (11-01-2005)

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Francis Comets, Francesco Guerra, Fabio Lucio Toninelli. The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature. Journal of Statistical Physics, 2005, 120, pp.147-165. ⟨10.1007/s10955-005-5471-1⟩. ⟨hal-00003866⟩
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