Cooperative phenomena in active matter systems with alternative interaction of neighbors

We investigate the impact of different nearest neighbor (NN) determination methods on flocking phase transitions in the Vicsek model. In addition to conventional methods (Cutoff, Voronoi, and k-NN), we implement a novel approach called 2D SANNex. While traditional metric-free methods like Voronoi maintain a constant transition point across varying densities, we demonstrate that both k-NN and 2D SANNex exhibit density-dependent transition shifts despite their metric-free nature. This unexpected behavior suggests that the metric-free property alone does not determine the density dependence of the transition points. Rather, we propose that the non-reciprocal characteristics inherent to k-NN and 2D SANNex methods play a crucial role in modulating the transition behavior.