Phase separation of self-propelled disks with ferromagnetic and nematic alignment

TL;DR

This paper investigates how ferromagnetic and nematic velocity alignments influence phase separation and order in self-propelled disks, combining microscopic theory with simulations to reveal the conditions fostering Motility-Induced Phase Separation.

Contribution

It develops a microscopic hydrodynamic theory for self-propelled disks with different alignment interactions and compares predictions with simulations, highlighting the distinct effects of ferromagnetic and nematic alignments on phase behavior.

Findings

Ferromagnetic alignment promotes phase separation via self-trapping.

Nematic alignment does not significantly affect phase separation.

The microscopic theory accurately predicts the stability and phase behavior.

Abstract

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and Motility-Induced Phase Separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a close set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in Motility-Induced Phase Separation.