  Motility-induced phase separation (MIPS) is a nonequilibrium phase separation
that has a different origin from equilibrium phase separation induced by
attractive interactions. Similarities and differences in collective behaviors
between these two types of phase separation have been intensely discussed.
Here, to study another kind of similarity between MIPS and attraction-induced
phase separation under a nonequilibrium condition, we perform simulations of
active Brownian particles with uniaxially anisotropic self-propulsion (uniaxial
ABPs) in two dimensions. We find that (i) long-range density correlation
appears in the homogeneous state, (ii) anisotropic particle configuration
appears in MIPS, where the anisotropy removes the possibility of microphase
separation suggested for isotropic ABPs [X.-Q. Shi et al., Phys. Rev. Lett.
125, 168001 (2020)], and (iii) critical phenomena for the anisotropic MIPS
presumably belong to the universality class for two-dimensional uniaxial
ferromagnets with dipolar long-range interactions. Properties (i)-(iii) are
common to the well-studied randomly driven lattice gas (RDLG), which is a
particle model that undergoes phase separation by attractive interactions under
external driving forces, suggesting that the origin of phase separation is not
essential for macroscopic behaviors of uniaxial ABPs and RDLG. Based on the
observations in uniaxial ABPs, we construct a coarse-grained Langevin model,
which shows properties (i)-(iii) and corroborates the generality of the
findings.
