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.

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Thermodynamic Limit in Mean Field Spin Glass Models
• Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model
• Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model