{"id":"openai-math/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model-September-24-2026","tags":["spin-glass","markov-chains","mixing-times"],"score":0,"title":"Critical slowing down in the Sherrington–Kirkpatrick model","domain":"Probability and statistical mechanics","family":"227","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Critical SK autocorrelation processes and dynamics across the temperature transition"}