{"paper":{"title":"Finite cycle Gibbs measures on permutations of $\\mathbb Z^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Florencia G. Leonardi, In\\'es Armend\\'ariz, Pablo A. Ferrari, Pablo Groisman","submitted_at":"2014-07-24T12:10:25Z","abstract_excerpt":"We consider Gibbs distributions on the set of permutations of $\\mathbb Z^d$ associated to the Hamiltonian $H(\\sigma):=\\sum_{x} V(\\sigma(x)-x)$, where $\\sigma$ is a permutation and $V:\\mathbb Z^d\\to\\mathbb R$ is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on $V$ ensuring that for large enough temperature $\\alpha>0$ there exists a unique infinite volume ergodic Gibbs measure $\\mu^\\alpha$ concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6542","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"}