Vicsek model of self-propelled particles with hybrid noise

Abstract

In self-propelled particle models, the interactions are generally subject to some type of noise, which is introduced either during or after the interactions between the particles. Here, self-propelled particles are subject to two different types of noise. If the orientation between them is less than a certain rate [Formula: see text], a vectorial noise is introduced in each particle–particle interaction, otherwise, an angular noise is introduced in the average direction of motion, already calculated, of neighboring particles. We vary the rate [Formula: see text] over a wide range ([Formula: see text]) and study the change in the nature of the phase transition. The product-moment correlation coefficient between the order parameter and the hybrid noise, is calculated. We found that in the combination of the two types of noise, the critical noise decreases with increasing the parameter [Formula: see text], and by analysis of the Binder cumulant we estimate the value of [Formula: see text] as from which begins to appear the effects of the vectorial noise on the phase transition.