{"paper":{"title":"First-Order Phase Transition in Potts Models with finite-range interactions","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Immacolata Merola, Thierry Gobron (LPTM)","submitted_at":"2006-09-18T13:21:17Z","abstract_excerpt":"We consider the $Q$-state Potts model on $\\mathbb Z^d$, $Q\\ge 3$, $d\\ge 2$, with Kac ferromagnetic interactions and scaling parameter $\\ga$. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for $\\ga$ small enough there is a value of the temperature at which coexist $Q+1$ Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for $d=2$, Q=3, in contrast with the case of nearest-neighbor interactions for which available results indicate a seco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0609051","kind":"arxiv","version":1},"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"}