Cluster-Mean-Field Approach to Short-Range Ising Spin Glasses in Replica Space

Abstract

We construct a cluster-mean-field theory for short-range spin glasses in the replica space, in which only the effective fields which are conjugate to the order parameters are taken into account. In the one-step replica-symmetry breaking (RSB) scheme just below the critical temperature, the solutions of the self-consistent equations for general clusters are given in terms of the thermal and quenched random averages of spin products. From the comparison of the free energies we have introduced, we find the (one-step) RSB solution is more stable than the replica-symmetric (RS) solution for arbitrary clusters so long as the former exists. Analytic solutions of the Bethe cluster approximation suggest that the RSB effects are rather enhanced by short-range fluctuations.