Scale free chaos in the confined Vicsek flocking model

TL;DR

This paper investigates a phase transition in a three-dimensional confined Vicsek model, revealing scale-free chaos characterized by criticality, with implications for understanding collective behavior in active matter systems.

Contribution

It identifies a new critical line of confinement versus noise where scale-free chaos emerges in the Vicsek model, extending understanding of phase transitions in active matter.

Findings

Existence of a critical line separating dispersed and multicluster swarms.

Scale-free chaos characterized by minimal correlation time and size-proportional correlation length.

Power-law behavior of susceptibility, correlation length, and Lyapunov exponent.

Abstract

The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite size effects and criticality in the three dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable `condensed' nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.