Criticality and the onset of ordering in the standard Vicsek model

Abstract

Experimental observations of animal collective behaviour have shown stunning evidence forthe emergence of large-scale cooperative phenomena resembling phase transitions in physicalsystems. Indeed, quantitative studies have found scale-free correlations and critical behaviourconsistent with the occurrence of continuous, second-order phase transitions. The standardVicsek model (SVM), a minimal model of self-propelled particles in which their tendencyto align with each other competes with perturbations controlled by a noise term, appearsto capture the essential ingredients of critical flocking phenomena. In this paper, we reviewrecent finite-size scaling and dynamical studies of the SVM, which present a full characteriz-ation of the continuous phase transition through dynamical and critical exponents. We alsopresent a complex network analysis of SVM flocks and discuss the onset of ordering inconnection with XY-like spin models.