Disorder-Induced Long-Ranged Correlations in Scalar Active Matter

TL;DR

This paper investigates how quenched disorder affects scalar active matter, revealing long-range correlations, a lower-critical dimension of 4, and different disorder regimes, challenging the typical phase separation behavior.

Contribution

It introduces a combined phenomenological and field-theoretical approach to identify disorder effects and the critical dimension in scalar active matter.

Findings

Motility-induced phase separation is replaced by long-range correlations in 2D.

A lower-critical dimension of 4 is identified for phase separation.

The structure factor scales as 1/q^2 in a weak-disorder regime.

Abstract

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