Cavity fields approach in spin glasses one step beyond

We improve the cavity fields approach for the Sherrington Kirkpatrick model of spin glasses in order to calculate correlation functions for spins in both the paramagnetic and glassy phases. This approach can be seen either as a stability check or as a tentative to compute finite-dimension corrections. We discuss also the zero modes that already appeared in the replica setting. In the glassy phase we again find zero modes (or better bands of modes) that may be related to the ones already found by De Dominicis and Kondor.