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

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

2005-01-11

arxiv.org/abs/math/0501164v1

Mathematics

Probability

Scientific paper

10.1007/s10955-005-5471-1

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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