Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles

One of the most popular approaches to the study of the collective behavior of self-driven individuals is the well-known Vicsek model (VM) [T. Vicsek, A. Cziroacutek, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)]. In the VM one has that each individual tends to adopt the direction of motion of its neighbors with the perturbation of some noise. For low enough noise the individuals move in an ordered fashion with net transport of mass; however, when the noise is increased, one observes disordered motion in a gaslike scenario. The nature of the order-disorder transition, i.e., first-versus second-order, has originated an ongoing controversy. Here, we analyze the most used variants of the VM unambiguously establishing those that lead either to first- or second-order behavior. By requesting the invariance of the order of the transition upon rotation of the observational frame, we easily identify artifacts due to the interplay between finite-size and boundary conditions, which had erroneously led some authors to observe first-order transitionlike behavior.