In this paper, we study numerically a short-range p-spin glass model in three dimensions. The behavior of the model appears to be remarkably different from mean-field predictions. In fact it shares some features typical of models with full replica symmetry breaking ͑FRSB͒. Nevertheless, we believe that the transition that we study is intrinsically different from the FRSB and basically due to nonperturbative contributions. We study both the statics and the dynamics of the system, which seem to confirm our conjectures.

In this work we discuss a short range version of the p-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and numerical simulation. We attribute it to non-perturbative effects due to the finite probability that each particular realization of the disorder allows for the formation of regions where the system is less frustrated and locally freezes at a higher temperature.

In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of additional corrections: these corrections can be interpreted as arising from fluctuations in the size of the blocks in the replica approach. The computation suggests a new approach for deriving the replica broken results in a rigorous way

Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence of a metastable saddle point in the replica formalism. An ansatz is made on the form of the metastable point and its contribution to the free energy is calculated. The Random Energy Model is considered along with the p-spin and the p-state Potts Models in their p < ∞ expansion.

In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the p = 2 spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation dissipation relation for the four-point correlation functions. This relation can be extended to the out of equilibrium regimes introducing a function Xt which, for large time t, as t −1/2 as in the case of the two-point functions.