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

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.

41 pages, reference added

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• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• On the overlap in the multiple spherical SK models
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