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

Abstract

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.