Spontaneously ordered motion of self-propelled particles

András Czirók, H. Eugene Stanley, Tamás Vicsek

Research output: Contribution to journalArticle

201 Citations (Scopus)


We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow, φ, emerges in this system in a phase-space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise η and the average density of the particles Q is calculated and is found to have the form ηc(ρ) ∼ ρ1/2. We also find that φ scales as a function of the external bias h (field or 'wind') according to a power law φ ∼ h0.9. In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.

Original languageEnglish
Pages (from-to)1375-1385
Number of pages11
JournalJournal of Physics A: Mathematical and General
Issue number5
Publication statusPublished - Mar 7 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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