{"paper":{"title":"Parallel spin wave for the Villain model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Paul Dario, Wei Wu","submitted_at":"2025-07-05T16:48:01Z","abstract_excerpt":"In this paper, we study the Villain model in $\\mathbb{Z}^d$ in dimension $d\\geq 3$. It is conjectured, that the parallel correlation function in the infinite volume Gibbs state, i.e., the map\n  $$\n  x \\mapsto \\langle \\cos\\theta(0) \\cos\\theta(x) \\rangle_{\\mu_{\\mathrm{Vil}, \\beta}} -\\left( \\langle \\cos\\theta(0) \\rangle_{\\mu_{\\mathrm{Vil}, \\beta}} \\right)^2,\n  $$\n  decays like $|x|^{-2(d-2)}$ as $|x| \\to \\infty$ at low temperature. The results of Bricmont, Fontaine, Lebowitz, Lieb, and Spencer (1981) show that for the related XY model, this correlation decays at least as fast as $|x|^{2-d}$. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04098","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04098/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}