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

TL;DR

This paper explores how run-and-tumble particles with attractive interactions exhibit re-entrant phase transitions and critical behavior, revealing a connection between nonequilibrium active matter and classical Ising universality.

Contribution

It demonstrates that motility-induced phase separation can be suppressed and re-entrant, with critical exponents matching equilibrium Ising models, establishing superuniversality in active matter.

Findings

Re-entrant phase separation occurs with increasing attraction.

Critical exponents vary continuously along the transition line.

Scaling functions match those of equilibrium Ising models.

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 passive systems. Here, we investigate RTPs in the presence of explicit attractive interactions and show that, at high motility, such interactions can suppress MIPS, yielding a homogeneous phase. Upon further increasing the attraction strength, phase separation reappears, giving rise to a re-entrant transition. We characterize this transition by analyzing the percolation properties of dense clusters, which provide geometric signatures of phase separation. Along the resulting critical line, we find continuously varying critical exponents, while certain scaling functions remain unchanged and coincide with those of equilibrium lattice gas models undergoing interacting percolation, which is in the Ising-percolation universality class. These results reveal that the MIPS transition in interacting RTP systems exhibit Ising superuniversality, thereby establishing a connection between nonequilibrium active matter and classical critical behavior.