{"paper":{"title":"On the general one-dimensional XY Model: positive and zero temperature, selection and non-selection","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":"A. O. Lopes, A. T. Baraviera, J. Mohr, L. M. Cioletti, R. R. Souza","submitted_at":"2011-06-14T23:46:40Z","abstract_excerpt":"We consider $(M,d)$ a connected and compact manifold and we denote by $\\mathcal{B}_i$ the Bernoulli space $M^{\\Z}$ of sequences represented by $$x=(... x_{-3},x_{-2},x_{-1},x_0,x_1,x_2,x_3,...),$$ where $x_i$ belongs to the space (alphabet) $M$. The case where $M=\\mathbb{S}^1$, the unit circle, is of particular interest here. The analogous problem in the one-dimensional lattice $\\mathbb{N}$ is also considered. %In this case we consider the potential $A: {\\cal B}=M^\\mathbb{N} \\to \\mathbb{R}.$ Let $A: \\mathcal{B}_i \\rar \\R$ be an {\\it observable} or {\\it potential} defined in the Bernoulli space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2845","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"}