  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 nonequilibrium 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.
