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 . In this paper, we revisit the original Vicsek model introduced in [Phys. Rev. Lett. 75, 1226] and demonstrate that the model lacks 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}
}