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.
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Guerra, F., Toninelli, F.L. The High Temperature Region of the Viana–Bray Diluted Spin Glass Model. Journal of Statistical Physics 115, 531–555 (2004). https://doi.org/10.1023/B:JOSS.0000019815.11115.54
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DOI: https://doi.org/10.1023/B:JOSS.0000019815.11115.54