Emergence of a single cluster in Vicsek's model at very low noise

Abstract

The classic Vicsek model [Phys. Rev. Lett. 75, 1226 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.1226] is studied in the regime of very low noise intensities, which is shown to be characterized by a cluster [macrocluster (MC)] that contains a macroscopic fraction of the system particles. It is shown that the well-known power-law behavior of the cluster-size distribution loses its cutoff, becoming bimodal at very low noise intensities: A peak develops for larger sizes to settle the emergence of the MC. The average cluster number m∗ is introduced as a parameter that properly describes this change, i.e., a line in the noise-speed phase portrait can be identified to separates both regimes. Finite-size scaling analysis is performed to show that a phase transition to a macroscopic cluster is taking place. Consistency of the results with the literature is also checked and commented on.