  We study spin glasses with Kac type interaction potential for small but
finite inverse interaction range $\gamma$. Using the theoretical setup of
coupled replicas, through the replica method we argue that the probability of
overlap profiles can be expressed for small $\gamma$ through a large-deviation
functional. This result is supported by rigorous arguments, showing that the
large-deviation functional provides at least upper bounds for the probability.
Finally we analyze the rate function, in the vicinity of the critical point
$T_c=1$ of mean field theory, and we study the free energy cost of overlap
interfaces, assuming the validity of a gradient expansion for the rate
functional.
