  We study the properties of fluctuation for the free energies and internal
energies of two spin glass systems that differ for having some set of
interactions flipped. We show that their difference has a variance that grows
like the volume of the flipped region. Using a new interpolation method, which
extends to the entire circle the standard interpolation technique, we show by
integration by parts that the bound imply new overlap identities for the
equilibrium state. As a side result the case of the non-interacting random
field is analyzed and the triviality of its overlap distribution proved.
