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Interaction-Flip Identities in Spin Glasses

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, 40127, Bologna, Italy

    Pierluigi Contucci

  2. Eindhoven University of Technology & EURANDOM, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Cristian Giardinà

  3. Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, 42100, Reggio Emilia, Italy

    Claudio Giberti

Authors
  1. Pierluigi Contucci
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  2. Cristian Giardinà
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  3. Claudio Giberti
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Correspondence to Pierluigi Contucci.

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Contucci, P., Giardinà, C. & Giberti, C. Interaction-Flip Identities in Spin Glasses. J Stat Phys 135, 1181–1203 (2009). https://doi.org/10.1007/s10955-009-9706-4

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  • DOI: https://doi.org/10.1007/s10955-009-9706-4

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