Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2006-11-15
Physica A 373 (2007) 445-454
Nonlinear Sciences
Adaptation and Self-Organizing Systems
13 pages, 11 figures
Scientific paper
10.1016/j.physa.2006.05.035
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 ($v\leq 0.1$). However, for large velocities ($v\geq 0.3$) 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.
Daruka Istvan
Nagy Máté
Vicsek Tamás
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