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We show that incompressible polar active fluids can exhibit an ordered,coherently moving phase even in the presence of quenched disorder in twodimensions. Unlike such active fluids with annealed (i.e., time-dependent)disorder only, which behave like equilibrium ferromagnets with long-rangeinteractions, this robustness against quenched disorder is a fundamentallynon-equilibrium phenomenon. The ordered state belongs to a new universalityclass, whose scaling laws we calculate using three different renormalizationgroup schemes, which all give scaling exponents within 0.02 of each other,indicating that our results are quite accurate. Our predictions can bequantitatively tested in readily available artificial active systems, and implythat biological systems such as cell layers can move coherently in vivo, wheredisorder is inevitable.

Packed swarms on dirt: two-dimensional incompressible flocks with quenched and annealed disorder