Site-bond percolation of polyatomic species

A generalization of the classical monomer site-bond percolation problem is studied in which linear k-uples of nearest neighbor sites (site k-mers) and linear k-uples of nearest neighbor bonds (bond k-mers) are independently occupied at random on a square lattice. We called this model the site-bond percolation of polyatomic species or k-mer site-bond percolation. Motivated by considerations of cluster connectivity, we have used two distinct schemes (denoted as S intersection of B and S union of B) for k-mer site-bond percolation. In S intersection of B(S union of B), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using Monte Carlo simulations and finite-size scaling theory, data from S intersection of B and S union of B are analyzed in order to determine the critical curves separating the percolating and nonpercolating regions.