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.
The high temperature region of the Viana-Bray diluted spin glass model / Guerra, Francesco; FABIO LUCIO, Toninelli. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 115:(2004), pp. 531-555. [10.1023/B:JOSS.0000019815.11115.54]
The high temperature region of the Viana-Bray diluted spin glass model
GUERRA, Francesco;
2004
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.