  We study through numerical simulation the Vicsek model for very low speeds
and densities. We consider scalar noise in 2-d and 3-d, and vector noise in
3-d. We focus on the behavior of the critical noise with density and speed,
trying to clarify seemingly contradictory earlier results. We find that, for
scalar noise, the critical noise is a power law both in density and speed, but
although we confirm the density exponent in 2-d, we find a speed exponent
different from earlier reports (we consider lower speeds than previous
studies). On the other hand, for the vector noise case we find that the
dependence of the critical noise cannot be separated as a product of power laws
in speed and density. Finally, we study the dependence of the relaxation time
with speed and find the same power law in 2-d and 3-d, with and exponent that
depends on whether the noise is above or below the critical value.
