We study the properties of fluctuation for the free energies and internalenergies of two spin glass systems that differ for having some set ofinteractions flipped. We show that their difference has a variance that growslike the volume of the flipped region. Using a new interpolation method, whichextends to the entire circle the standard interpolation technique, we show byintegration by parts that the bound imply new overlap identities for theequilibrium state. As a side result the case of the non-interacting randomfield is analyzed and the triviality of its overlap distribution proved.
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