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We study through numerical simulation the Vicsek model for very low speedsand densities. We consider scalar noise in 2-d and 3-d, and vector noise in3-d. We focus on the behavior of the critical noise with density and speed,trying to clarify seemingly contradictory earlier results. We find that, forscalar noise, the critical noise is a power law both in density and speed, butalthough we confirm the density exponent in 2-d, we find a speed exponentdifferent from earlier reports (we consider lower speeds than previousstudies). On the other hand, for the vector noise case we find that thedependence of the critical noise cannot be separated as a product of power lawsin speed and density. Finally, we study the dependence of the relaxation timewith speed and find the same power law in 2-d and 3-d, with and exponent thatdepends on whether the noise is above or below the critical value.

Self-propelled Vicsek particles at low speed and low density