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

EZEQUIEL V ALBANO; GABRIEL BAGLIETTO,

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2009 vol. 80 p. 50103 - 50107

1063-651X

One of the most popular approaches to the study of the collective behavior of self-driven individuals is thewell-known Vicsek model
VM T. Vicsek, A. Czirók, 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 itsneighbors with the perturbation of some noise. For low enough noise the individuals move in an orderedfashion with net transport of mass; however, when the noise is increased, one observes disordered motion in agaslike scenario. The nature of the order-disorder transition, i.e., first-versus second-order, has originated anongoing controversy. Here, we analyze the most used variants of the VM unambiguously establishing thosethat lead either to first- or second-order behavior. By requesting the invariance of the order of the transitionupon rotation of the observational frame, we easily identify artifacts due to the interplay between finite-size andboundary conditions, which had erroneously led some authors to observe first-order transitionlike behavior.