Re-entrant percolation in active Brownian hard disks

TL;DR

This study reveals a non-monotonic, re-entrant percolation behavior in active Brownian hard disks, driven by the interplay of activity-induced attraction and cluster breakup, with implications for understanding non-equilibrium clustering.

Contribution

It introduces the concept of re-entrant percolation in active matter and develops an effective potential mapping to passive systems, highlighting structural differences beyond pair correlations.

Findings

Weak activity lowers percolation threshold

Further activity causes re-entrant percolation behavior

Active and passive systems have similar radial distributions but differ in higher-order correlations

Abstract

Non-equilibrium clustering and percolation are investigated in an archetypal model of two-dimensional active matter using dynamic simulations of self-propelled Brownian repulsive particles. We concentrate on the single-phase region up to moderate levels of activity, before motility-induced phase separation (MIPS) sets in. Weak activity promotes cluster formation and lowers the percolation threshold. However, driving the system further out of equilibrium partly reverses this effect, resulting in a minimum in the critical density for the formation of system-spanning clusters and introducing re-entrant percolation as a function of activity in the pre-MIPS regime. This non-monotonic behaviour arises from competition between activity-induced effective attraction (which eventually leads to MIPS) and activity-driven cluster breakup. Using an adapted iterative Boltzmann inversion method, we derive effective potentials to map weakly active cases onto a passive (equilibrium) model with conservative attraction, which can be characterised by Monte Carlo simulations. While the active and passive systems have practically identical radial distribution functions, we find decisive differences in higher-order structural correlations, to which the percolation threshold is highly sensitive. For sufficiently strong activity, no passive pairwise potential can reproduce the radial distribution function of the active system.