New interpretation of Parisi-Sompolinsky mean-field solution for spin glasses

Using real replicas to describe the many-state phase space of the Sherrington-Kirkpatrick model of a spin glass, we rederive the Sompolinsky free energy for the ground state. We propose an interpretation of the order parameter function q(x), x 0,1, from the Sompolinsky free energy directly within the real replica scheme. We also suggest an iterative way of reaching the ground-state (Sompolinsky) free energy within this scheme and present numerical results for the first iteration going beyond the ergodic (replica symmetric) solution.The authors are grateful to the referee for constructive comments leading to improvements in the construction of the Sompolinsky free energy and the following interpretation.