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 (ps,pb) 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.