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 γ0. This could be a first step toward an expansion around mean field theory, for spin glass systems.
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