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

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

2003-02-20

arxiv.org/abs/cond-mat/0302401v1

Journal of Statistical Physics Volume 115, Numbers 1-2, pp. 531-555 (2004).

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages

Scientific paper

10.1023/B:JOSS.0000019815.11115.

In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. 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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