Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together

John Toner and Yuhai Tu
Phys. Rev. Lett. 75, 4326 – Published 4 December 1995
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Abstract

We propose a nonequilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly nontrivial, and different from the equilibrium model, for d<dc=4; nonetheless, we are able to determine its scaling exponents exactly in d=2 and show that, unlike equilibrium systems, our model exhibits a broken continuous symmetry even in d=2. Our model describes a large universality class of microscopic rules, including those recently simulated by Vicsek et al.

  • Received 9 June 1995

DOI:https://doi.org/10.1103/PhysRevLett.75.4326

©1995 American Physical Society

Authors & Affiliations

John Toner1,2 and Yuhai Tu1,*

  • 1IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598
  • 2Department of Physics, University of Oregon, Eugene, Oregon 97403-1274

  • *Current address.

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Vol. 75, Iss. 23 — 4 December 1995

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