Absence of O(2) symmetry in the Vicsek model.

Authors

Yushin Takahashi, Kota Mitsui, Tsuyoshi Mizohata, Hideyuki Miyahara

Published in

Physical review. E. Volume 114. Issue 1-1. Pages 014134.

Abstract

The phase transition in the Vicsek model is widely believed to be associated with spontaneous symmetry breaking of the two-dimensional rotational symmetry O(2). In this paper, we revisit the original model introduced by Vicsek et al. [Phys. Rev. Lett. 75, 1226 (1995)0031-900710.1103/PhysRevLett.75.1226] 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. As a consequence, we numerically demonstrate that the phase transition reported in the original paper vanishes when the global phase is adaptively chosen.

PMID:
42629923
Bibliographic data and abstract were imported from PubMed on 22 Aug 2026.

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