Umbral de percolación en las redes de Kagomé y Dice

Abstract

An alternative way to calculate percolation thresholds of bonds and sites on Kagome (K) and Dice (D) lattices are presented. The methodology used is based on considering the topological structures of these lattices and characterize them by a polynomial function provided by the simplest structures, as are the square lattice (C), the triangular lattice (T), and the hexagonal lattice (H). To obtain the polynomial functions associated to C, T, and H, the technique associated to the growth of small cells is used to determine the exact finite occupation of bonds (or sites). The percolation threshold is obtained through two methods in order to compare and validate results. Techniques related to finite size of lattices are used, including the asymptotic corrections to the laws of scale in each case. The technique allows independently know the percolation threshold for both the problem of bonds, such as sites. The results obtained for the bond (site) percolation threshold for the K lattice is $ 0.52440516 $ ($ 0.65270365 $) and for D lattice is $ 0.47559502 $ ($ 0.58504625 $).