Slow Equilibration and Persistent Stationary Correlations in Spherical Spin Glasses
We study the Langevin dynamics of spherical mixed $p$-spin glasses at fixed temperature, on time scales exponential in the dimension $N$. Below the static transition temperature, the dynamics started from the uniform distribution on the sphere stays at total variation distance close to one from the Gibbs measure up to a time exponential in $N$, with probability tending to one. We prove this for pure models of degree at least four at every such temperature, and for mixtures of minimum degree at least four that satisfy an explicit condition on a function of one variable. It extends to initial…
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