# Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model

@article{Guerra2002CentralLT,
title={Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model},
author={Francesco Guerra and Fabio L. Toninelli University of Rome 'La Sapienza' and Infn and Rom{\'e} and Scuola Normale Superiore Pisa and Pisa},
journal={Journal of Mathematical Physics},
year={2002},
volume={43},
pages={6224-6237}
}
• Published 8 January 2002
• Mathematics
• Journal of Mathematical Physics
In a region above the Almeida–Thouless line, where we are able to control the thermodynamic limit of the Sherrington–Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale 1/N, for large N. The method we employ is based on the idea we recently developed of introducing quadratic coupling between two replicas. The proof makes use of the cavity equations and of concentration of measure inequalities for the…

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### Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model

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### Higher Order Expansions for the Overlap of the SK Model

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### A Central Limit Theorem for a Localized Version of the SK Model

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We develop a very simple method to study the high temperature, or equivalently high external field, behavior of the Sherrington–Kirkpatrick mean field spin glass model. The basic idea is to couple

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We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps