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

GONZÁLEZ-FLORES, M. I.; TORRES, A. A.; LEBRECHT, W.; RAMIREZ-PASTOR, A. J.

Physical Review E

APS

Año: 2021 vol. 104

2470-0045

The site-bond percolation problem in two-dimensional kagome lattices has been studied by means of theoreticalmodeling and numerical simulations. Motivated by considerations of cluster connectivity, two distinctschemes (denoted as S ∩ B and S ∪ B) have been considered. In S ∩ B (S ∪ B), two points are connected if asequence of occupied sites and (or) bonds joins them. Analytical and simulation approaches, supplemented byanalysis using finite-size scaling theory, were used to calculate the phase boundaries between the percolating andnonpercolating regions, thus determining the complete phase diagram of the system in the (ps, pb) space. In thecase of the S ∩ B model, the obtained results are in excellent agreement with previous theoretical and numericalpredictions. In the case of the S ∪ B model, the limiting curve separating percolating and nonpercolating regionsis reported here.