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

Iain M. Johnstone, Yegor Klochkov, Alexei Onatski, Damian Pavlyshyn

Published 2021-04-15Version 1

This paper studies fluctuations of the free energy of the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J \in [0,1)$ and inverse temperature $\beta$. We consider the critical temperature regime $\beta=1+bN^{-1/3}\sqrt{\log N}$, $b\in\mathbb{R}$. For $b \leq 0$, the limiting distribution of the free energy is Gaussian. As $b$ increases from $0$ to $\infty$, we describe the transition of the limiting distribution from Gaussian to Tracy-Widom.