Dimer site-bond percolation on a square lattice

Abstract

A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are independently occupied at random on a square lattice is studied. We called this model as dimer 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 dimer 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 finite-size scaling theory, data from $S \cap B$ and $S \cup B$ are analyzed in order to determine i) the phase boundary between the percolating and non-percolating regions and ii) the numerical values of the critical exponents of the phase transition occurring in the system. The results obtained are discussed in comparison with the corresponding ones for classical monomer site-bond percolation.