{"paper":{"title":"Absence of $\\mathrm{O} (2)$ symmetry in the Vicsek model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hideyuki Miyahara, Kota Mitsui, Tsuyoshi Mizohata, Yushin Takahashi","submitted_at":"2026-04-01T14:08:25Z","abstract_excerpt":"The phase transition in the Vicsek model is widely believed to be associated with spontaneous symmetry breaking of the two-dimensional rotational symmetry $\\mathrm{O} (2)$.\n  In this paper, we revisit the original Vicsek model introduced by Vicsek \\textit{et al.} [Phys.~Rev.~Lett.~75,~1226~(1995)] and demonstrate that the original angle-based update rule is not invariant under global phase shifts at the level of angular increments when it is implemented using the principal-value arctangent, as in the original definition.\n  As a consequence, we numerically demonstrate that the phase transition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.00930","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/2604.00930/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"}