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We consider disorder-order phase transitions in the three-dimensional versionof the scalar noise model (SNM) of flocking. Our results are analogous to thosefound for the two-dimensional case. For small velocity (v <= 0.1) a continuous,second-order phase transition is observable, with the diffusion of nearbyparticles being isotropic. By increasing the particle velocities the phasetransition changes to first order, and the diffusion becomes anisotropic. Thefirst-order transition in the latter case is probably caused by the interplaybetween anisotropic diffusion and periodic boundary conditions, leading to aboundary condition dependent symmetry breaking of the solutions.

Phase transition in the scalar noise model of collective motion in three dimensions