Cooperative phenomena in active matter systems with alternative interaction of neighbors

Graduate School of Engineering, Nagoya Institute of Technology, 466-8555, Japan

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 12 September 2025

Abstract

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.