Three-body Interactions Drive the Transition to Polar Order in a Simple Flocking Model

Active systems are characterized by a discontinuous flocking transition from a disordered isotropic state to a polar ordered state with increasing density and decreasing noise. A large class of mesoscopic or macroscopic theories for flocking are coarse grained from microscopic models that feature binary interactions as the chief aligning mechanism. However, at the high densities at which the system flocks, binary interactions are too weak to account for the ordering transition. Here we introduce a solvable one-dimensional model of flocking, and derive a series of approximations for the stochastic hydrodynamics. We show that three-body interactions are not only necessary but also sufficient to capture the full phenomenology of flocking.