Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

The site-bond percolation problem in two-dimensional kagome lattices has been studied by means of theoretical modeling and 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 connected if a sequence of occupied sites and (or ) bonds joins them. Analytical and simulation approaches, supplemented by analysis using finite-size scaling theory, were used to calculate the phase boundaries between the percolating and nonpercolating regions, thus determining the complete phase diagram of the system in the (p_s,p_b ) space. In the case of the S ∩B model, the obtained results are in excellent agreement with previous theoretical and numerical predictions. In the case of the S ∪B model, the limiting curve separating percolating and nonpercolating regions is reported here.