Conferencia Invitada. On the collective behavior of self-driven individuals

EZEQUIEL V ALBANO; GABRIEL BAGLIETTO,

San luis de Potosi

Workshop; XII Latin American Workshop on Nonlinear Phenomena (LAWNP-2011); 2011

The Vicsek model
VM T. Vicsek et al., Phys. Rev. Lett. 75, 1226
1995, for the description of thecollective behavior of self-driven individuals, assumes that each of them adopts the average direction ofmovement of its neighbors, perturbed by an external noise. A second-order transition between a state of orderedcollective displacement
low-noise limit and a disordered regime
high-noise limit was found early on.However, this scenario has recently been challenged by Grégory and Chaté G. Grégory and H. Chaté, Phys.Rev. Lett. 92, 025702
2004 who claim that the transition of the VM may be of first order. By performingextensive simulations of the VM, which are analyzed by means of both finite-size scaling methods and adynamic 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 independentmethods—i.e., stationary and dynamic measurements—we provide two tests showing that the standard hyperscalingrelationship d
−2 = holds, where ,
, and  are the order parameter, correlation length, and“susceptibility” critical exponents, respectively. Furthermore, we established that at criticality, the correlationlength grows according to t1/z, with z1.27
3, independently of the degree of order of the initial configuration,in marked contrast with the behavior of the XY model.