{"paper":{"title":"Glauber Dynamics for the mean-field Potts Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Allan Sly, Eyal Lubetzky, Jian Ding, Oren Louidor, Paul Cuff, Yuval Peres","submitted_at":"2012-04-19T23:50:56Z","abstract_excerpt":"We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability.\n  We prove that when $\\beta<\\beta_s(q)$ the mixing time is asymptotically $C(\\beta, q) n \\log n$ and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order $n$. At $\\beta=\\beta_s(q)$ the dynamics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4503","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":""},"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"}