{"paper":{"title":"Systematic scanning Glauber dynamics for the mean-field Ising model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Sanghak Jeon","submitted_at":"2023-07-19T16:49:17Z","abstract_excerpt":"We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \\leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly randomly chosen permutations over the $k$ vertices. We show that if $k = o(n^{1/3})$, the high temperature regime $\\beta < 1$ exhibits cutoff phenomena. For critical temperature regime $\\beta = 1$, We prove that the mixing time is of order $n^{3/2}k^{-1}$. For $\\beta > 1$, we prove the mixing time is of order $nk^{-1}\\log n$ under the restricted dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10127","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.10127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}