Spin glass to paramagnetic transition in Spherical Sherrington-Kirkpatrick model with ferromagnetic interaction

This paper studies fluctuations of the free energy of the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant J ∈ [0, 1) and inverse temperature β. We consider the critical temperature regime β = 1 + bN−1/3 √ log N , b ∈ R. For b ≤ 0, the limiting distribution of the free energy is Gaussian. As b increases from 0 to ∞, we describe the transition of the limiting distribution from Gaussian to Tracy-Widom.

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