Abstract:
We analyze extensions of the TAP (Thouless, Anderson, Palmer) mean-field free energy for spin glases by means of the so-called real replicas. With a small interaction between the replicas we break their independence and derive a TAP-like free energy with new order parameters. We then average this extended TAP free energy over random spin-spin interactions in the replica symmetric manner. From the solution of the resulting saddle-point equations for two replicas we deduce the symmetry of the matrix of the order parameters. Using this symmetry restriction we rewrite our equations and solve them for three and four replicas. We finally analytically continue the equations to arbitrary number of replicas. We find that the Parisi one-step replica symmetry breaking (1RSB) solution is thereby reproduced.