We consider a finite-range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance ${\gamma }^{-1}$. We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit $\gamma \to 0$. This could be a first step toward an expansion around mean-field theory, for spin glass systems.

• Received 16 October 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.030602