Banded phases in topological flocks

Abstract

Flocking phase transitions arise in many aligning active soft matter systems, and an interesting question concerns the role of “topological” vs. “metric” interactions on these transitions. While recent theoretical work suggests that the order–disorder transition in these polar aligning models is universally first order, numerical studies have suggested that topological models may instead have a continuous transition. Some recent simulations have found that some variations of topologically interacting flocking agents have a discontinuous transition, but unambiguous observations of phase coexistence using common Voronoi-based alignment remains elusive. In this work, we use a custom GPU-accelerated simulation package to perform million-particle-scale simulations of a Voronoi–Vicsek model in which alignment interactions stem from an XY-like Hamiltonian. By accessing such large systems on appropriately long time scales and in the time-continuous limit, we are able to show a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.