  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.
