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We study a finite range spin glass model in arbitrary dimension, where theintensity of the coupling between spins decays to zero over some distance$\gamma^{-1}$. We prove that, under a positivity condition for the interactionpotential, the infinite-volume free energy of the system converges to that ofthe Sherrington-Kirkpatrick model, in the Kac limit $\gamma\to0$. We study theimplication of this convergence for the local order parameter, i.e., the localoverlap distribution function and a family of susceptibilities to itassociated, and we show that locally the system behaves like its mean fieldanalogue. Similar results are obtained for models with $p$-spin interactions.Finally, we discuss a possible approach to the problem of the existence of longrange order for finite $\gamma$, based on a large deviation functional foroverlap profiles. This will be developed in future work.Comment: 19 pages, revtex

Finite-range spin glasses in the Kac limit: free energy and local observables