The most famous math we’ve used for years to explain how birds fly in flocks has been found to be fundamentally wrong.
April 2, 2026
Original Paper
Absence of $O (2)$ symmetry in the Vicsek model
arXiv · 2604.00930
The Takeaway
For 30 years, the 'Vicsek model' was the gold standard for understanding how thousands of animals coordinate their movement. This study reveals the model lacks a basic symmetry everyone assumed was there, suggesting that our understanding of how order emerges from chaos in nature needs a total rethink.
From the 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.