We study a model of self-propelled particles interacting with their
k
nearest neighbors through polar alignment. By exploring its phase space as a
function of two nondimensional parameters (alignment strength
g and Peclet
number
Pe), we identify two distinct order-disorder transitions. One
is 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/gα, 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.