Percolation of defective dimers irreversibly deposited on honeycomb and triangular lattices

Abstract

The percolation problem of irreversibly deposited dimers on honeycomb and triangular lattices is studied. A dimer is composed of two segments, and occupies two adjacent adsorption 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. Different cases were investigated, according to the types of dimers involved in the process. By means of numerical simulations and finite-size scaling techniques, the complete phase diagram separating the percolating from the nonpercolating regions was determined for each considered lattice. The present results are compared with the previous study of deposition of defective dimers on square lattices.