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

Abstract

The classic Vicsek model [Phys.Rev.Lett. {\bf75},1226(1995)] is studied in the regime of very low noise intensities, which is shown to be characterized by a cluster (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. The average largest cluster parameter also develops large fluctuations at a non zero critical noise. 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 upon.

References in corpus (7)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
• Pattern formation mechanisms in motility mutants of Myxococcus xanthus
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units

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