Alternating steady state in one-dimensional flocking

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous non-equilibrium phase transition from a condensed phase, in which a single 'flock' contains a finite fraction of the particles. to a homogeneous phase: we study the transition using numerical finite-size scaling. Surprisingly. in the condensed phase the steady state is alternating, with the mean direction of motion of particles reversing stochastically on a timescale proportional to the logarithm of the system size. We present a simple argument to explain this logarithmic dependence. We argue that the reversals are essential to the survival of the condensate. Thus, the discrete directional symmetry is not spontaneously broken.