How Continuous Symmetry Stabilizes the Ordered Phase of Polar Flocks

TL;DR

This paper investigates how continuous symmetry in polar flock models enhances the stability of the ordered phase by preventing the growth of destabilizing droplets, contrasting with discrete-symmetry models.

Contribution

It demonstrates that continuous symmetry can stabilize the ordered phase at low noise levels, revealing a lower critical dimension than discrete-symmetry models.

Findings

Continuous symmetry destabilizes droplet edges, preventing growth.

Ordered phase stability depends on symmetry type and noise level.

Continuous-symmetry models have a lower critical dimension.

Abstract

We study the stability of the ordered phase of compressible polar flocks against the nucleation of counter-propagating droplets, using a combination of analytical theory, microscopic and hydrodynamic simulations. For discrete-symmetry flocks, such droplets are known to always grow and propagate, making the ordered phase metastable. We explain how, on the contrary, continuous symmetry can stabilize the ordered phase at small enough noise by destabilizing the leading edge of growing droplets. Flocking models with continuous symmetries thus have a lower critical dimension than their discrete-symmetry counterparts, in contrast to equilibrium physics.