Fluctuation-induced phase separation in metric and topological models of collective motion

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turns changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including the topological models in which particles interact with a fixed number of nearest neighbors, which were believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.