The Ising-Sherrington-Kirpatrick model in a magnetic field at high   temperature
  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. 
Francis Comets (PMA), Francesco Guerra (Fisica, Roma 1), Fabio Lucio   Toninelli (Phys-ENS)