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

Máté Nagy, István Daruka and Tamás Vicsek

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 445-454

Abstract: 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.

Keywords: Collective motion; Self-propelled particles; Phase transitions; Nonequilibrium systems (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:445-454

DOI: 10.1016/j.physa.2006.05.035

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