LETTER TO THE EDITOR: Alternating steady state in one-dimensional flocking

  title={LETTER TO THE EDITOR: Alternating steady state in one-dimensional flocking},
  author={O. J. O'Loan and Martin R. Evans},
  journal={Journal of Physics A},
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… 

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  • 1998
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