Self-propelled hard disks: implicit alignment and transition to collective motion

TL;DR

This paper investigates the phase transition from isotropic to collective motion in self-propelled hard disks, revealing a distinct transition mechanism from the Vicsek model and explaining it through Boltzmann theory.

Contribution

It demonstrates a novel discontinuous transition in self-propelled hard disks and provides a theoretical explanation based on binary scattering properties, contrasting with the Vicsek model.

Findings

Discontinuous transition from isotropic to polar phase at zero noise.

Transition becomes continuous at a tri-critical point with increasing noise.

Differences in phase behavior originate from distinct scattering physics.

Abstract

We show that low density homogeneous phases of self propelled hard disks exhibit a transition from isotropic to polar collective motion, albeit of a qualitatively distinct class from the Vicsek one. In the absence of noise, an abrupt discontinuous transition takes place between the isotropic phase and a fully polar absorbing state. Increasing the noise, the transition becomes continuous at a tri-critical point. We explain all our numerical findings in the framework of Boltzmann theory, on the basis of the binary scattering properties. We show that the qualitative differences observed between the present and the Vicsek model at the level of their phase behavior, take their origin in the complete opposite physics taking place during scattering events. We argue that such differences will generically hold for systems of self-propelled particles with repulsive short range interactions.