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 $S\cap B$ and $S\cup B$) for $k$-mer site-bond percolation. In $S\cap B(S\cup B)$, 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 $S\cap B$ and $S\cup B$ are analyzed in order to determine the critical curves separating the percolating and nonpercolating regions.

• Received 31 May 2005

DOI:https://doi.org/10.1103/PhysRevE.72.066129