Percolation in a simple cubic lattice with distortion

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.