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arXiv · 1505.07349

Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model

Jinho Baik·Ji Oon Lee
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Abstract

The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in the high temperature regime the law of the fluctuations converges to the Gaussian distribution just like in the Sherrington-Kirtkpatrick model. We show, on the other hand, that the law of the fluctuations is given by the GOE Tracy-Widom distribution in the low temperature regime. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.

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Jinho Baik, Ji Oon Lee. 2015-07-05. Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model. https://doi.org/10.1007/s10955-016-1610-0

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