| Abstract: | We study the stability of the ordered phase of flocking models that break either a discrete or a continuous symmetry. For flocks that break a discrete symmetry, 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 spread ballistically in all directions. The result implies that, in the thermodynamic limit, discrete-symmetry flocks—and, by extension, continuous-symmetry flocks with rotational anisotropy—are globally unstable in all dimensions. In contrast, using the active XY model and a hydrodynamic description, we find flocks that break an isotropic continuous symmetry to be globally stable, albeit within a qualitatively narrower region of the phase diagram compared to previous studies. The results imply that, in contrast to equilibrium systems, breaking a continuous symmetry is easier than a discrete one.
|
