Banded phases in topological flocks

TL;DR

This study uses large-scale GPU simulations to demonstrate that topological flocking models exhibit a discontinuous phase transition with stable phase coexistence, confirming the first-order nature of the transition.

Contribution

It provides the first unambiguous evidence of phase coexistence in topological flocking models through million-particle simulations.

Findings

Stable phase coexistence observed between ordered and disordered phases.

Transition confirmed to be discontinuous (first order) in the thermodynamic limit.

Large-scale simulations crucial for revealing the true nature of the transition.

Abstract

Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by which agents are considered to be interacting neighbors. 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 these Voronoi-Vicsek flocking models. By accessing such large systems on appropriately long time scales, we are able to show that a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.