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 mode l 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 effe cts due to the finite probability that each particular realization of the d isorder allows for the formation of regions where the system is less frustr ated and locally freezes at a higher temperature. [S0163-1829(99)02501-1].