Emergent Metric-like States of Active Particles with Metric-free Polar Alignment

We study a model of self-propelled particles interacting with their k-nearest neighbors via polar alignment. By exploring the phase space as a function of two nondimensional parameters (scaled alignment strength and Peclet number), we identify two distinct order-disorder transitions. One appears to be continuous, occurs at a low critical g value independent of Pe, and resembles a mean-field transition with no density-order coupling. The other is discontinuous, depends on a combined control parameter involving g and Pe, and results from the formation of small, dense, highly persistent clusters of particles that follow metric-like dynamics. These dense clusters form at a critical value of the combined control parameter Pe/g^α, with α≈1.5, which appears to be valid for different alignment-based models. Our study shows that models of active particles with metric-free interactions can produce characteristic length-scales and self-organize into metric-like collective states that undergo metric-like transitions.