{"paper":{"title":"Mixing Phases and Metastability for the Glauber Dynamics on the p-Spin Curie-Weiss Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jiang Zhang, Ramkrishna Jyoti Samanta, Somabha Mukherjee","submitted_at":"2024-12-22T10:12:40Z","abstract_excerpt":"The Glauber dynamics for the classical $2$-spin Curie-Weiss model on $N$ nodes with inverse temperature $\\beta$ and zero external field is known to mix in time $\\Theta(N\\log N)$ for $\\beta < \\frac{1}{2}$, in time $\\Theta(N^{3/2})$ at $\\beta = \\frac{1}{2}$, and in time $\\exp(\\Omega(N))$ for $\\beta >\\frac{1}{2}$. In this paper, we consider the $p$-spin generalization of the Curie-Weiss model with an external field $h$, and identify three disjoint regions almost exhausting the parameter space, with the corresponding Glauber dynamics exhibiting three different orders of mixing times in these regio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16952","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/2412.16952/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"}