Moving together while breaking Newton’s third law: how nonreciprocal interactions influence collective motion

The Vicsek model is a paradigmatic model of active matter, providing a minimal framework that captures the physics of collective motion, or flocking.

In recent years, it has become apparent that nonreciprocal interactions — interactions that violate Newtons third law— are a defining feature of out-of-equilibrium systems like active matter.

We study how nonreciprocal interactions affect collective motion by extending the Vicsek model to two species which interact nonreciprocally. Using numerical simulations together with an analysis of the corresponding coarse-grained continuum equations, we show that even weak nonreciprocal alignment leads to large-scale structure formation in flocking mixtures. Strikingly, the emergence of these structures is accompanied by demixing of the species, despite the absence of repulsive interactions.

Our theoretical analysis reveals the origin of the instability and demonstrates that it is a generic feature of nonreciprocal flocks.