Polar flock in the presence of random quenched rotators

TL;DR

This paper investigates how random quenched rotators affect the ordering of polar self-propelled particles, revealing a transition from long-range to quasi-long-range order and then to disorder, with theoretical predictions of anisotropic fluctuations.

Contribution

It introduces a model combining polar flock dynamics with quenched rotators, analyzing the impact on order and fluctuations, bridging equilibrium XY and Vicsek models.

Findings

Quenched rotators destroy long-range order in polar flocks.

System exhibits quasi-long-range order at moderate rotator density.

Transition from quasi-long-range order to disorder occurs at a critical rotator density.

Abstract

We study a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate in the presence of random quenched rotators. These rotators act like obstacles which rotate the orientation of the SPPs by an angle determined by their intrinsic orientations. In the zero self-propulsion limit, our model reduces to the equilibrium $XY$ model with quenched disorder, while for the clean system, it is similar to the Vicsek model for polar flock. We note that a small amount of the quenched rotators destroys the long-range order usually noted in the clean SPPs. The system shows a quasi-long range order state upto some moderate density of the rotators. On further increment in the density of rotators, the system shows a continuous transition from the quasi-long-range order to disorder state at some critical density of rotators. Our linearized hydrodynamic calculation predicts anisotropic higher order fluctuation in two-point structure factors for density and velocity fields of the SPPs. We argue that nonlinear terms probably suppress this fluctuation such that no long-range order but only a quasi-long-range order prevails in the system.