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Experimental observations of animal collective behavior have shown stunningevidence for the emergence of large-scale cooperative phenomena resemblingphase transitions in physical systems. Indeed, quantitative studies have foundscale-free correlations and critical behavior consistent with the occurrence ofcontinuous, second-order phase transitions. The Standard Vicsek Model (SVM), aminimal model of self-propelled particles in which their tendency to align witheach other competes with perturbations controlled by a noise term, appears tocapture the essential ingredients of critical flocking phenomena. In thispaper, we review recent finite-size scaling and dynamical studies of the SVM,which present a full characterization of the continuous phase transitionthrough dynamical and critical exponents. We also present a complex networkanalysis of SVM flocks and discuss the onset of ordering in connection withXY-like spin models.

Criticality and the Onset of Ordering in the Standard Vicsek Model