Percolation in a simple cubic lattice with distortion

TL;DR

This study investigates how site percolation thresholds in a simple cubic lattice are affected by systematic and random distortions, revealing that the thresholds depend on the connection criteria and maintaining universality class.

Contribution

It introduces a model of site percolation with lattice distortion and analyzes how the percolation threshold varies with distortion and connection threshold.

Findings

Percolation threshold increases with distortion when connection threshold ≥ lattice constant.

Threshold first decreases then increases with distortion if connection threshold < lattice constant.

Percolation in distorted and regular lattices share the same universality class.

Abstract

Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular positions. The amount of distortion is tunable by a parameter called the distortion parameter. In this model, two occupied neighboring sites are considered connected only if the distance between them is less than a predefined value called the connection threshold. It is observed that the percolation threshold always increases with distortion if the connection threshold is equal to or greater than the lattice constant of the regular lattice. On the other hand, if the connection threshold is less than the lattice constant, the percolation threshold first decreases, then increases steadily as distortion is increased. It is shown that the variation of the percolation threshold can be well explained by the change in the fraction of occupied bonds with distortion. The values of the relevant critical exponents of the transition strongly indicate that percolation in regular and distorted simple cubic lattices belong to the same universality class. It is also demonstrated that this model is intrinsically distinct from the site-bond percolation model.