Site-bond percolation of heteronuclear dimers irreversibly deposited on square lattices

Abstract

A generalization of the site-bond percolation problem was studied, in which pairs of neighboring sites (site dimers) and bonds are occupied irreversibly, randomly, and independently on homogeneous square surfaces. A dimer is composed of two segments and occupies two adjacent sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Two types of dimers are considered, AA and AB, and the connectivity analysis is carried out by accounting only for the conductive segments (segments type A) in combination with bonds. For the combination of dimers and bonds, two different criteria were analyzed: the union or the intersection between the adsorbed percolating particles and the bonds. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a non-percolating region was determined.

Percolation of defective dimers irreversibly deposited on honeycomb and triangular lattices

“…1 Equivalent configurations can be obtained by initially depositing all dimers on the lattice up to desirable total concentration θ T = θ AB + θ AA , and then randomly differentiating these dimers on AB and AA types according to their concentration [27,28].…”

“…For this purpose, extensive numerical simulations have been performed to study the percolation of dimers composed of segments A and B deposited on triangular and honeycomb lattices. The results obtained are discussed and compared with data from square lattices [27,28].…”

“…Two previous articles [27,28], referred to as papers I and II, respectively, were devoted to the study of percolation of heteronuclear dimers irreversibly deposited on square lattices. In paper I, a site percolation model of defective (or heteronuclear) dimers was investigated.…”