Absence of $O (2)$ symmetry in the Vicsek model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915905849524224 |
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| author | Takahashi, Yushin Mitsui, Kota Mizohata, Tsuyoshi Miyahara, Hideyuki |
| author_facet | Takahashi, Yushin Mitsui, Kota Mizohata, Tsuyoshi Miyahara, Hideyuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00930 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Absence of $O (2)$ symmetry in the Vicsek model Takahashi, Yushin Mitsui, Kota Mizohata, Tsuyoshi Miyahara, Hideyuki Statistical Mechanics Biological Physics 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. |
| title | Absence of $O (2)$ symmetry in the Vicsek model |
| topic | Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2604.00930 |