New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion

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In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder-order transition in the SNM is a continuous, second order phase transition for small particle velocities (v ≤ 0.1). However, for large velocities (v ≥ 0.3) we find a strong anisotropy in the particle diffusion in contrast with the isotropic diffusion for small velocities. The interplay between the anisotropic diffusion and the periodic boundary conditions leads to an artificial symmetry breaking of the solutions (directionally quantized density waves) and a consequent first order transition like behavior. Thus, it is not possible to draw any conclusion about the physical behavior in the large particle velocity regime of the SNM.

Original languageEnglish
Pages (from-to)445-454
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - Jan 1 2007



  • Collective motion
  • Nonequilibrium systems
  • Phase transitions
  • Self-propelled particles

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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