Alternating steady state in one-dimensional flocking
arXiv:cond-mat/9811336 · doi:10.1088/0305-4470/32/8/002
Abstract
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.
8 pages LaTeX2e, 5 figures. Uses epsfig and IOP style. Submitted to J. Phys. A (Math. Gen.)
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