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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.
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