Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems

TL;DR

This study combines percolation theory and Monte Carlo simulations to analyze anisotropic percolation in Janus disks, revealing that their critical behavior aligns with isotropic percolation after spatial rescaling, applicable to other anisotropic systems.

Contribution

It demonstrates that anisotropic percolation in Janus particles can be understood through isotropic percolation models via spatial rescaling, extending to other anisotropic systems.

Findings

Percolation threshold depends on patch size and temperature.

Critical clusters are elongated along stripe directions.

Rescaling aligns anisotropic percolation with isotropic universality class.

Abstract

We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the $q$-state Potts model with anisotropic interactions.