Finite-size scaling analysis and dynamic study of the critical behavior of a model for the collective displacement of self-driven individuals

GABRIEL BAGLIETTO,; EZEQUIEL V ALBANO

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

American Physical Society

Año: 2008 vol. 78 p. 21125 - 21134

1063-651X

The Vicsek model (VM, Vicsek et al. Phys. Rev. Lett. {f75}, 1226 (1995)) for the description of the collective behavior of self-driven individuals, assumes that each of them adopts the average direction of movement of its neighbors, perturbed by an external noise.A second-order transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) has early been found.However, this scenario has recently been challenged by Gr´egory and Chat´e (Gr´egory and Chat´e, Phys. Rev. Lett. {f92}, 025702 (2004)) who claim that the transition of the VM may be of first order. By performing extensive simulations of the VM, which are analyzed by means of both finite-size scaling methods and a dynamic scaling approach, we unambiguously demonstrate  the critical nature of the transition. Furthermore, the complete set of critical exponents of the VM, in $d=2$ dimensions, is determined. By means of independent methods, i.e. stationary and dynamic measurements, we provide two tests showing that the standard hyperscaling relationship $ d u-2eta=gamma$ holds, where $eta$, $ u$ and $gamma$ are the order parameter, correlation length and ``susceptibility´´ critical exponents, respectively.Furthermore, we established that at criticality, the correlation length grows according to $ xisim t^{1/z}$, with $zsimeq 1.27(3)$ independently of the degree of order of the initial configuration, in marked contrast with the behavior of the XY model.