Impact of Higher-Order Interactions on Collective Motion

Abstract

Collective motion in self-propelled particle systems has been widely studied using the Vicsek model, which relies on pairwise alignment interactions. We introduce a generalized Vicsek model that incorporates higher-order (triadic) alignment interactions. Using agent-based simulations and mean-field theory, we demonstrate that pure triadic alignment induces a discontinuous phase transition, evidenced by hysteresis, a double-well free-energy landscape, and a Binder cumulant minimum that deepens with system size, whereas the standard pairwise model exhibits a continuous transition at the same system sizes. We further show that higher-order interactions require higher particle densities to sustain collective order and produce sharper fluctuation peaks near the transition with lower critical noise. These results establish that the microscopic structure of the alignment interaction, whether pairwise or many-body, is an independent control parameter for the order of the phase transition in active matter, with implications for understanding collective behavior in biological and synthetic systems.