Stacked triangular lattice: Percolation properties

The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid-state physics and materials science, its percolation properties have received little attention. We investigate several nonuniversal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is pcᵇᵒⁿᵈ=0.18602±0.00002 for bonds and pcˢⁱᵗᵉ=0.26240±0.00005 for sites. The number of clusters at the threshold per site is ncᵇᵒⁿᵈ=0.28458±0.00005 and ncˢⁱᵗᵉ=0.03998±0.00005. The stacked triangular lattice is a convenient choice to study the RGB model [Schrenk et al., Sci. Rep. 2, 751 (2012)]. We present results on this model and its scaling behavior at the percolation threshold.