{"paper":{"title":"Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Heng Guo, Jiaheng Wang, Weiming Feng","submitted_at":"2022-05-04T10:32:41Z","abstract_excerpt":"We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01985","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/2205.01985/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"}