English

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

Statistical Mechanics 2026-04-02 v1 Biological Physics

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)O (2). In this paper, we revisit the original Vicsek model introduced in [Phys. Rev. Lett. 75, 1226] and demonstrate that the model lacks O(2)O (2) symmetry. As a consequence, we numerically demonstrate that the phase transition reported in the original paper vanishes when the global phase is adaptively chosen.

Keywords

Cite

@article{arxiv.2604.00930,
  title  = {Absence of $O (2)$ symmetry in the Vicsek model},
  author = {Yushin Takahashi and Kota Mitsui and Tsuyoshi Mizohata and Hideyuki Miyahara},
  journal= {arXiv preprint arXiv:2604.00930},
  year   = {2026}
}