Geometric and Nonequilibrium Criticality in Run-and-Tumble Particles with Competing Motility and Attraction

Abstract: Self-propulsion in run-and-tumble particles (RTPs) generates effective attractive interactions that can drive motility-induced phase separation (MIPS), a phenomenon absent in their passive counterparts. In this work, we show that at high motility, introducing explicit attractive interactions among RTPs can suppress MIPS, leading to a homogeneous phase, and subsequently induce a re-emergence of phase separation at stronger attraction --thus realizing a reentrant phase transition. We characterize this transition by examining the percolation properties of dense clusters, which serve as geometric signatures of phase separation. Along the resulting critical line, we observe continuously varying critical exponents, while some of the associated scaling functions remain invariant and coincide with those of equilibrium lattice gas models undergoing interacting percolation, which is Ising-percolation universality. These findings reveal that the phase separation transition in interacting RTPs exhibits Ising-like super universality, bridging nonequilibrium active matter with classical critical behavior.