A VARIATIONAL APPROACH TO ISING SPIN-GLASSES IN FINITE DIMENSIONS

We introduce a hierarchical class of approximations of the random Isin g spin glass in d dimensions. The attention is focused on finite clust ers of spins where the action of the rest of the system is properly ta ken into account. At the lowest level (cluster of a single spin) our a pproximation coincides with the SK model while at the highest level it coincides with the true d-dimensional system. The method is variation al and it uses the replica approach to spin glasses and the Parisi ans atz for the order parameter. As a result we have rigorous bounds for t he quenched free energy which become more and more precise when larger and larger clusters are considered.