{"paper":{"title":"Fractional Vortices, $\\mathbb{Z}_2$ Gauge Theory, and the Confinement-Deconfinement Transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Dung-Hai Lee, Yen-Ta Huang, Zhi-Qiang Gao","submitted_at":"2022-04-26T17:53:59Z","abstract_excerpt":"In this paper we discuss the classical 3D XY model whose nearest-neighbor interaction is a mixture of $\\cos(\\theta_i-\\theta_j)$ (ferromagnetic) and $\\cos2(\\theta_i-\\theta_j)$ (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a non-compact $U(1)$ gauge field (the \"EM\" interaction), the half-vortices interact with an extra interaction mediated by a $\\mathbb{Z}_2$ gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the 't Hooft loops and their mutual statistic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12482","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.12482/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"}