Interaction-Flip Identities in Spin Glasses |
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Authors: | Pierluigi Contucci Cristian Giardinà Claudio Giberti |
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Affiliation: | 1. Dipartimento di Matematica, Università di Bologna, 40127, Bologna, Italy 2. Eindhoven University of Technology & EURANDOM, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands 3. Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, 42100, Reggio Emilia, Italy
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Abstract: | 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. |
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