Dimer site-bond percolation on a triangular lattice

Abstract

A generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means of numerical simulations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S ∩ B and S ∩ B) have been considered. In S ∪ B (S ∪ B), two points are said to be connected if a sequence of occupied sites and ( or) bonds joins them. Numerical data, supplemented by analysis using finite-size scaling theory, were used to determine (i) the complete phase diagram of the system (phase boundary between the percolating and nonpercolating regions), and (ii) the values of the critical exponents (and universality) characterizing the phase transition occurring in the system.