Phase separation and emergence of collective motion in a one-dimensional system of active particles.

We study numerically a one-dimensional system of self-propelled particles, where the state of the particles is given by their moving direction (left or right), which is encoded by a spin-like variable, and their position. Particles interact by short-ranged, spring-like attractive forces and do not possess spin-spin interactions (i.e., velocity alignment). Newton's third law is broken in this model by assuming an asymmetric interaction range that is larger in the direction of the moving direction of the particle. We show that in this nonequilibrium system, due to the absence of the action-reaction symmetry, there exists an intimate link between phase separation and the formation of highly coherent, spatially localized, moving flocks (i.e., collective motion). More specifically, we prove the existence of two fundamentally different types of active phase separation, which we refer to as neutral phase separation (NPS) and polar phase separation. Furthermore, we indicate that NPS is subdivided in two classes with distinct critical exponents. These results are of key importance to understand that in active matter, there exist several phase-separation classes and that the emergence of polar, self-organized patterns (i.e., flocks) does not require the presence of a velocity alignment.