Critical Motility-Induced Phase Separation in Three Dimensions is Consistent with Ising Universality

TL;DR

This study uses large-scale simulations and theoretical analysis to show that the critical behavior of motility-induced phase separation in 3D active particles aligns with the well-known 3D Ising universality class, indicating similar critical properties to passive fluids.

Contribution

It provides the first comprehensive numerical and theoretical evidence that 3D MIPS belongs to the 3D Ising universality class, resolving debates on the nature of active critical phenomena.

Findings

Critical exponents match 3D Ising class

Finite-size scaling confirms universality

Hydrodynamic theory flows to Wilson-Fisher fixed point

Abstract

Identifying the universality class of critical active phase transitions has been the subject of recent interest and controversy. Resolving these controversies will require robust numerical investigations to determine whether active critical exponents point to novel universality classes or are consistent with established ones. Here, we conduct large-scale computer simulations and a finite-size scaling analysis of the motility-induced phase separation (MIPS) of active Brownian hard spheres in three dimensions (3D), finding that the static and dynamic critical exponents all closely match those of the 3D Ising universality class with a conserved scalar order parameter. This finding is corroborated by a fluctuating hydrodynamic description of the critical dynamics of the order parameter field which flows to the Wilson-Fisher fixed point in three dimensions. Our work suggests that 3D MIPS and likely the entire phase diagram of active Brownian hard spheres is similar to that of molecular passive fluids despite the absence of Boltzmann statistics.