Cluster approximation for Ising spin glasses

We report about a new variational method [9] which approximates in a hierarchical way the random Ising spin glass on lattice in d dimensions. At the lon est level our approximation coincides with the Sherrington-Kirkpatrick model, while at the highest level it coincides with the true d-dimensional system. The attention is focused on finite size clusters of spins where the action of the rest of the system is taken into account by a coupling field, which is the variational parameter of the problem.