Swarming in the Dirt: Ordered Flocks with Quenched Disorder

TL;DR

This paper investigates how quenched disorder affects the collective motion of active particles, revealing that active polar systems are more resilient than equilibrium ferromagnets, maintaining order even in disordered environments.

Contribution

It demonstrates that active polar systems sustain long-range order in three dimensions and quasi-long-range order in two dimensions despite quenched disorder, unlike equilibrium systems.

Findings

Active polar systems maintain order in 3D with quenched disorder.

In 2D, active systems show quasi-long-range order under disorder.

Simulations confirm theoretical predictions for 2D behavior.

Abstract

The effect of quenched (frozen) disorder on the collective motion of active particles is analyzed. We find that active polar systems are far more robust against quenched disorder than equilibrium ferromagnets. Long ranged order (a non-zero average velocity $\langle{\bf v}\rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$; in $d=2$, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs. In equilibrium systems, only quasi-long-ranged order in $d=3$ and short ranged order in $d=2$ are possible. Our theoretical predictions for two dimensions are borne out by simulations.