Universality class of the motility-induced phase separation critical point
In plain words
Self-propelled particles that only repel each other can still separate into a dense crowd and a dilute gas, called motility-induced phase separation (MIPS). Whether the critical point where the two phases merge behaves like the ordinary liquid-gas (Ising) critical point is disputed.
Precise statement
Active Brownian particles with purely repulsive interactions phase separate above a critical Peclet number $\mathrm{Pe}_{\mathrm{c}}$ (ratio of self-propulsion to thermal diffusion). Determine the critical exponents $\nu, \beta$ and $\gamma/\nu$ at the MIPS critical point in $d = 2$ and decide whether they equal 2D Ising values or define a different universality class. An answer combines finite-size scaling with controlled corrections and a renormalization-group analysis of the coarse-grained field theory (active model $B+$). In 3D, MIPS coexistence near the critical point is metastable against crystallization (Omar et al. 2021), so the 3D question concerns a metastable critical point.
What would settle it
Finite-size scaling of the order-parameter distribution at $\mathrm{Pe}_{c}$ in systems large enough to control corrections, consistent with a renormalization-group calculation.
Status in the literature
Unverified note
Large-scale 2D studies (Partridge and Lee 2019; Maggi et al. 2021) and a 2025 3D study find Ising exponents, against an earlier non-Ising report (Siebert et al. 2018); no renormalization-group calculation for active model B+ confirms Ising universality.