Disorder-Induced Long-Ranged Correlations in Scalar Active Matter

We study the impact of quenched random potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two dimensions by an asymptotically homogeneous with anomalous long-ranged correlations nonvanishing steady-state currents. Using a combination phenomenological models field-theoretical treatment, we show existence lower-critical dimension ${d}_{c}=4$, below which only observed for systems smaller than Imry-Ma length scale. identify weak-disorder regime structure factor scales as $S(q)\ensuremath{\sim}1/{q}^{2}$, accounts our numerics. In $d=2$, predict that, at larger scales, behavior should cross over to strong-disorder regime. $d>2$, these regimes exist separately, depending strength potential.