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We study a model of self-propelled particles interacting with their $k$nearest neighbors through polar alignment. By exploring its phase space as afunction of two nondimensional parameters (alignment strength $g$ and Pecletnumber $\mathrm{Pe}$), we identify two distinct order-disorder transitions. Oneis continuous, occurs at a low critical $g$ value independent of Pe, andresembles a mean-field transition with no density-order coupling. The other isdiscontinuous, depends on a combined control parameter involving $g$ and Pe,and results from the formation of small, dense, highly persistent clusters ofparticles that follow metric-like dynamics. These dense clusters form at acritical value of the combined control parameter $\mathrm{Pe}/g^{\alpha}$, with$\alpha \approx 1.5$, which appears to be valid for different alignment-basedmodels. Our study shows that models of active particles with metric-freeinteractions can produce characteristic length-scales and self-organize intometric-like collective states that undergo metric-like transitions.

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