Critical slowing down in the Sherrington–Kirkpatrick model

At the critical inverse temperature β = 1, we prove slow mixing for zero-field Gaussian Sherrington–Kirkpatrick heat-bath dynamics from typical equilibrium configurations held fixed as initial states. For every deterministic sequence $t_n=o(n^{2/3})$ in rate-one-per-site time, the Gibbs mass of initial states whose time-t${}_n$ total-variation distance from equilibrium exceeds 1/4 tends to one in probability over the disorder. The same statement holds for every deterministic integer sequence $k_n=o(n^{5/3})$ of uniform-site update attempts.