On the Spectral Gap of Spherical Spin Glass Dynamics

Abstract

We consider the time to equilibrium for the Langevin dynamics of the spherical $p$-spin glass model of system size $N$. We show that the log-Sobolev constant and spectral gap are order $1$ in $N$ at sufficiently high temperature whereas the spectral gap decays exponentially in $N$ at sufficiently low temperatures. These verify the existence of a dynamical high temperature phase and a dynamical glass phase at the level of the spectral gap. Key to these results are the understanding of the extremal process and restricted free energy of Subag--Zeitouni and Subag.

21 pages

References in corpus (3)

• Theoretical perspective on the glass transition and amorphous materials
• The geometry of the Gibbs measure of pure spherical spin glasses
• Limiting dynamics for spherical models of spin glasses at high temperature

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