### Abstract

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 η_{c}(ρ) ∼ ρ^{1/2}. We also find that φ scales as a function of the external bias h (field or 'wind') according to a power law φ ∼ h^{0.9}. In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.

Original language | English |
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Pages (from-to) | 1375-1385 |

Number of pages | 11 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 30 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 7 1997 |

### ASJC Scopus subject areas

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

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## Cite this

*Journal of Physics A: Mathematical and General*,

*30*(5), 1375-1385. https://doi.org/10.1088/0305-4470/30/5/009