Some comments on the connection between disordered long range spin glass models and their mean field version

In this paper, we consider a particular aspect of the relationship between mean field and finite-dimensional spin glasses. By means of a simple interpolation method, we prove that the free energy of a class of finite-dimensional spin glass models with Kac-type interactions is bounded below by that of their mean field analogue. As a result, Parisi theory of replica symmetry breaking can be exploited in order to give bounds on their free energy and ground state energy. Similar results hold for diluted versions of the systems