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

TL;DR

This paper shows that the Vicsek model does not possess $O(2)$ symmetry as previously believed, and the associated phase transition disappears when the global phase is adaptively chosen.

Contribution

It reveals the absence of $O(2)$ symmetry in the Vicsek model and demonstrates the disappearance of the phase transition under certain conditions.

Findings

The Vicsek model lacks $O(2)$ symmetry.

The phase transition vanishes with adaptive global phase.

Original phase transition claims are challenged.

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