{"id":"openai-math/Critical-mixing-in-the-Sherrington-Kirkpatrick-model","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026","tags":["spin-glass","markov-chains","mixing-times"],"score":0,"title":"Critical mixing 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 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Critical SK autocorrelation processes and dynamics across the temperature transition"}