{"id":"openai-math/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase","pdf":"https://github.com/openai/math/blob/main/preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Cutoff-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026","tags":["spin-glass","markov-chains","mixing-times"],"score":0,"title":"Cutoff throughout the high-temperature Sherrington–Kirkpatrick phase","domain":"Probability and statistical mechanics","family":"227","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove worst-case total-variation cutoff for the zero-field Gaussian Sherrington–Kirkpatrick heat-bath dynamics at every fixed inverse temperature $`0\\leq\\beta\\lt 1`$. With rate-one refresh at each spin, the cutoff location is $`\\log n/(2\\lambda(\\beta))`$ for a positive deterministic rate $`\\lambda(\\beta)`$. The location for uniformly chosen single-site update attempts is n times as large. Convergence is in probability over the disorder.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Critical SK autocorrelation processes and dynamics across the temperature transition"}