Bond percolation thresholds for the Kagome and diced lattices

Abstract

Using a necessary condition for the star-triangle transformation, the author determines the percolation thresholds for the bond problem on the Kagome and diced lattices from those of the honeycomb and triangular lattices. He obtains the threshold for the Kagome lattice: PK*=0.498460; and that for the diced lattice: pd*=0.501540. He notes that although his estimation values seem to be quite reasonable, they may still not be exact.