  We study a finite range spin glass model in arbitrary dimension, where the
intensity of the coupling between spins decays to zero over some distance
$\gamma^{-1}$. We prove that, under a positivity condition for the interaction
potential, the infinite-volume free energy of the system converges to that of
the Sherrington-Kirkpatrick model, in the Kac limit $\gamma\to0$. We study the
implication of this convergence for the local order parameter, i.e., the local
overlap distribution function and a family of susceptibilities to it
associated, and we show that locally the system behaves like its mean field
analogue. Similar results are obtained for models with $p$-spin interactions.
Finally, we discuss a possible approach to the problem of the existence of long
range order for finite $\gamma$, based on a large deviation functional for
overlap profiles. This will be developed in future work.
