The Kac limit for finite-range spin glasses

Abstract

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 $γ^{-1}$. 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 $γ\to0$. This could be a first step toward an expansion around mean field theory, for spin glass systems.