Percolation of defective dimers irreversibly deposited on honeycomb, square and triangular lattices

Abstract

The percolation problem of irreversibly deposited heteronuclear dimers on square, honeycomb and triangular lattices is studied. Also, a generalization of the site-bond percolation problem was treated, in which pairs of neighboring sites (site dimers) and bonds are occupied irreversibly, randomly, and independently on the surface. A dimer is composed of two segments, and it occupies two adjacent lattice sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Three types of dimers are considered: AA, BB, and AB. The connectivity analysis is carried out by accounting only for the conductive segments (segments type A), whereas the B segments occupy a site in the lattice but are not taken into account in the percolation study. 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 nonpercolating region was determined for each case. In order to analyze the universality of the studied systems, the critical exponents were also calculated.