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}
}
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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  • Mathematics
    Journal of Statistical Physics
  • 2021
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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