Critical motility-induced phase separation belongs to the Ising universality class

Active matter is an extreme kind of non-equilibrium system in that detailed balance is broken at the microscopic scale. A typical active system can be a collection of particles that continuously exert mechanical forces on their surrounding environment, and systems of interacting active particles can display novel phenomena, ranging from the emergence of collective motion in two dimensions when the active particles are aligning, to motility-induced phase separation (MIPS) when the particles interact solely via volume exclusion interactions. However, even though active matter breaks detailed balance in a fundamental way, it remains unclear whether the hydrodynamic, universal behavior of active matter necessarily differs from that of equilibrium systems. The investigation of universal behavior, besides being of central interest to physics, allows us to transfer knowledge of a well-known system to a different system of novel interest. Here, we do exactly that by demonstrating that the critical behaviour of MIPS belongs to the Ising universality class with conservative dynamics. We do so using three approaches: hydrodynamic argument, field-theoretic description of a microscopic model, and simulation of a lattice model.