Finite-dimensional corrections to the mean field in a short-range p-spin glassy model

In this work we discuss a short range version of the p-spin model. The model is provided with a parameter that allows us to control the crossover with the mean field behavior. We detect a discrepancy between the perturbative approach and numerical simulations. We attribute it to nonperturbative 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. [S0163-1829(99)02501-1].