Spin-glass stochastic stability : a rigorous proof

P. Contucci, C. Giardinà

    Research output: Contribution to journalArticleAcademicpeer-review

    36 Citations (Scopus)

    Abstract

    We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spinglass quenched state. We show that stochastic stability holds in ß-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show that the volume rate at which the property is reached in the thermodynamic limit is V-1. As a byproduct we show that the stochastic stability identities coincide with those obtained with a different method by Ghirlanda and Guerra when applied to the thermal fluctuations only.
    Original languageEnglish
    Pages (from-to)915-923
    JournalAnnales Henri Poincaré : A Journal of Theoretical and Mathematical Physics
    Volume6
    Issue number5
    DOIs
    Publication statusPublished - 2005

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