We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model,...

We consider fluctuations of the local magnetic field in frustrated mean-field Ising models. Frustration can come about due to randomness of the interaction as in the Sherrington-Kirkpatrick model, or through fixed interaction parameters but with varying signs. We consider central limit theorems for the fluctuation of the local magnetic field values w.r.t. the a priori spin distribution for both...

We develop a cavity method in the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As an application we carry out second moment computations for the overlap and magnetization.