{"paper":{"title":"Selection of measure and a Large Deviation Principle for the general XY model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jairo Mengue","submitted_at":"2011-06-15T23:14:02Z","abstract_excerpt":"We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\\mathbb{N}}$. The shift acting on $X$ is denoted by $\\sigma$.\n  We analyze the general XY model, as presented in a recent paper by A. T. Baraviera, L. M. Cioletti, A. O. Lopes, J. Mohr and R. R. Souza. Denote the Gibbs measure by $\\mu_{c}:=h_{c}\\nu_{c}$, where $h_{c}$ is the eigenfunction, and, $\\nu_{c}$ is the eigenmeasure of the Ruelle operator associated to $cf$. We are going to prove that any measure selected by $\\mu_{c}$, as $c\\to +\\infty$, is a maximizing measure for $f$. We also show, when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3118","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"}