{"paper":{"title":"The effect of boundary conditions on mixing of 2D Potts models at discontinuous phase transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eyal Lubetzky, Reza Gheissari","submitted_at":"2017-01-01T00:37:32Z","abstract_excerpt":"We study Swendsen--Wang dynamics for the critical $q$-state Potts model on the square lattice. For $q=2,3,4$, where the phase transition is continuous, the mixing time $t_{\\textrm{mix}}$ is expected to obey a universal power-law independent of the boundary conditions. On the other hand, for large $q$, where the phase transition is discontinuous, the authors recently showed that $t_{\\textrm{mix}}$ is highly sensitive to boundary conditions: $t_{\\textrm{mix}} \\geq \\exp(cn)$ on an $n\\times n$ box with periodic boundary, yet under free or monochromatic boundary conditions, $t_{\\textrm{mix}} \\leq\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00181","kind":"arxiv","version":4},"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"}