Swarming and Flocking Unified Through Aggregation

Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their velocities align as a byproduct of achieving stable cohesion. In our framework, individuals move in open space and possess differing self-propelling velocities. Furthermore, velocity fluctuations are triggered by individual errors when following the aggregation rules. Notably, the system exhibits scale invariance, which is shown to be rooted in the model's definition -- a feature that we label as structural criticality. Finally, we show the emergence of a striking regime where spatial and orientational coherence decouple. That is, the system can achieve states of high and low polarization while maintaining spatial homogeneity.