Emergent Metric-like States of Active Particles with Metric-free Polar Alignment

TL;DR

This paper investigates a model of active particles with metric-free polar alignment, revealing two types of phase transitions and the emergence of metric-like collective states with characteristic length-scales.

Contribution

It demonstrates that metric-free interaction models can produce metric-like states and transitions, expanding understanding of active matter behavior.

Findings

Identified a continuous order-disorder transition independent of density.

Discovered a discontinuous transition involving dense cluster formation.

Found that the critical parameter for cluster formation scales as Pe/g^1.5.

Abstract

We study a model of self-propelled particles interacting with their $k$ nearest neighbors through polar alignment. By exploring its phase space as a function of two nondimensional parameters (alignment strength $g$ and Peclet number $\mathrm{Pe}$), we identify two distinct order-disorder transitions. One is continuous, occurs at a low critical $g$ value independent of Pe, and resembles a mean-field transition with no density-order coupling. The other is discontinuous, depends on a combined control parameter involving $g$ and Pe, and results from the formation of small, dense, highly persistent clusters of particles that follow metric-like dynamics. These dense clusters form at a critical value of the combined control parameter $\mathrm{Pe}/g^{\alpha}$, with $\alpha \approx 1.5$, which appears to be valid for different alignment-based models. Our study shows that models of active particles with metric-free interactions can produce characteristic length-scales and self-organize into metric-like collective states that undergo metric-like transitions.