Metastability of Discrete-Symmetry Flocks

Abstract

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks -- and, by extension, continuous-symmetry flocks with rotational anisotropy -- are metastable in all dimensions.