On the spectral gap of spherical spin glass dynamics
R Gheissari, A Jagannath - 2019 - projecteuclid.org
2019•projecteuclid.org
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
at sufficiently high temperatures 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 …
model of system size N. We show that the log-Sobolev constant and spectral gap are order 1
at sufficiently high temperatures 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 …
Abstract
We consider the time to equilibrium for the Langevin dynamics of the spherical -spin glass model of system size . We show that the log-Sobolev constant and spectral gap are order at sufficiently high temperatures whereas the spectral gap decays exponentially in 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.
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