Non-universality in the 2D flocking model

Abstract

In this paper, we discuss the universality of the critical exponents β and δ found in the Viscek model for one zone of interaction in the 2D flocking model. Within the framework of this model, the particles move with the same absolute velocity v0 and interact locally by trying to align their direction with that of neighbors. In this paper, we include a second zone of interaction named zone of repulsion R1, where each agent attempts to maintain a minimum distance from the others. Our model results show that in order to maintain an order in a flock with higher density, it is necessary to decrease the region of repulsion around each individual. Depending on the noise and on the density, the order parameter va is found to scale as [Formula: see text] and [Formula: see text], respectively. Our findings show that the exponents β and δ depend strongly on the size of the repulsion zone and on the density ρ, indicating the non-universality of these critical exponents. The analysis is performed over different situations by using a numerical simulation technique.