Computer simulations of the collective displacement of self-propelled agents

We report extensive computer simulations of the Vicsek model [V.M. Vicsek, et al., Phys. Rev. Lett. 75 (1995) 1226], aimed to describe the onset of ordering within the low-velocity regime of the collective displacement of self-driven agents. The VM assumes that each agent adopts the average direction of movement of its neighbors, perturbed by an external noise. The existence of a phase transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) is most likely the most distinctive feature of the VM. In this paper, after briefly discussing the critical nature of the transition we focus our attention on the behavior of the VM in the low-velocity (v0→0v0→0) regime for the displacement of the agents. In fact, while the XY model, which could somewhat be considered as the equilibrium counterpart of the VM, does not exhibit order in d=2d=2 dimensions, an intriguing feature of the VM is precisely the onset of order. Since in the XY model the particles remain fixed in the lattice, we show that the understanding of the v0→0v0→0 limit is relevant in order to explain the different behavior of both models.