The high temperature region of the Viana-Bray diluted spin glass model

F. Guerra, F.L. Toninelli

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    Abstract

    In this paper, we study the high temperature or low connectivity phase of the Viana–Bray model in the absence of magnetic field. This is a diluted version of the well known Sherrington–Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a complete control of the system, proving annealing for the infinite volume free energy and a central limit theorem for the suitably rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy fluctuations, on the scale 1/N, converge in the infinite volume limit to a non-Gaussian random variable, whose variance diverges at the boundary of the replica-symmetric region. The connection with the fully connected Sherrington– Kirkpatrick model is discussed.
    Original languageEnglish
    Pages (from-to)531-555
    JournalJournal of Statistical Physics
    Volume115
    Issue number1-2
    DOIs
    Publication statusPublished - 2004

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