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arXiv · 1709.01499

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

Lucas Barberis
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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.

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Lucas Barberis. 2018-07-04. Emergence of a single cluster in Vicsek's model at very low noise. https://doi.org/10.1103/physreve.98.032607

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