Critical mixing in the Sherrington–Kirkpatrick model

At the critical inverse temperature β = 1, we determine the worst-start total-variation mixing exponent for single-site heat-bath dynamics in the zero-field Gaussian Sherrington–Kirkpatrick model. The mixing time is $n^{2/3+o(1)}$ when every site has rate one, or $n^{5/3+o(1)}$ attempted uniform-site updates, in probability over the disorder.