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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 (\(v\leq 0.1\)). 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.