{"id":"openai-math/Stretched-exponential-barriers-for-typical-SK-initial-states","pdf":"https://github.com/openai/math/blob/main/preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Stretched-exponential-barriers-for-typical-SK-initial-states-September-24-2026","tags":["statistical-physics","spin-glass","sherrington-kirkpatrick","mixing-time"],"score":0,"title":"Stretched-exponential barriers for typical SK initial states","domain":"Probability and statistical mechanics","family":"227","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"At every fixed inverse temperature β > 1, we prove a stretched-exponential obstruction to mixing for the zero-field Sherrington–Kirkpatrick model from typical equilibrium configurations held fixed as initial states. The Gibbs mass of states whose total-variation distance from equilibrium at time $`\\exp(n^{1/10000})`$ exceeds 1/4 tends to one in probability over the disorder. This holds for rate-one-per-site heat-bath dynamics and after the same stated number of discrete update attempts.","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"}