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Emergent Symmetry in Constant-Density Flocks
Abstract
In two dimensions, the ordered phase of constant-density flocks is described by a single angle field, which makes them arguably the simplest systems with a scale-free ordered phase of collective motion. We show that the equation governing the corresponding Nambu-Goldstone mode, completed with terms previously discarded, possesses on large scales an invariance combining a shear and a Galilean boost. Broken at the bare level, this symmetry is restored at the unique attractive fixed point, and the associated Ward identities fix the scaling exponents exactly, as confirmed numerically.
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BibTeX
@misc{chate2026emergent,
title = {{Emergent Symmetry in Constant-Density Flocks}},
author = {Hugues Chaté and Alexandre Solon},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07771},
eprint = {2611.07771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07771},
}
RIS
TY - UNPB
TI - Emergent Symmetry in Constant-Density Flocks
AU - Hugues Chaté
AU - Alexandre Solon
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07771
UR - https://arxiv.org/abs/2611.07771
AB - In two dimensions, the ordered phase of constant-density flocks is described by a single angle field, which makes them arguably the simplest systems with a scale-free ordered phase of collective motion. We show that the equation governing the corresponding Nambu-Goldstone mode, completed with terms previously discarded, possesses on large scales an invariance combining a shear and a Galilean boost. Broken at the bare level, this symmetry is restored at the unique attractive fixed point, and the associated Ward identities fix the scaling exponents exactly, as confirmed numerically.
ER -