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

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.

6+10 pages, 4+14 figures

References in corpus (15)

• Recent advances in percolation theory and its applications
• Recent advances and open challenges in percolation
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• Orientationally Glassy Crystals of Janus Spheres
• Emergence of Multiscale Dynamics in Colloidal Gels
• Critical surfaces for general bond percolation problems
• Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• Bond percolation thresholds on Archimedean lattices from critical polynomial roots
• Percolation in the canonical ensemble
• Connectivity, Not Density, Dictates Percolation in Nematic Liquid Crystals of Slender Nanoparticles
• Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\ge 2$ Dimensions
• Universal Critical Wrapping Probabilities in the Canonical Ensemble
• Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model
• Percolation thresholds of randomly rotating patchy particles on Archimedean lattices

Cited by in corpus (1)

• Universality of the complete-graph Potts model with $0<q\le 2$