Stacked triangular lattice: Percolation properties

Abstract

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 few attention. We investigate several non-universal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is $p_c^{\text{bond}}=0.18602\pm 0.00002$ for bonds and $p_c^{\text{site}}=0.26240\pm 0.00005$ for sites. The number of clusters at the threshold per site is $n_c^{\text{bond}}=0.28458\pm 0.00005$ and $n_c^{\text{site}}=0.03998\pm 0.00005$. The stacked triangular lattice is a convenient choice to study the RGB model [Sci. Rep. {\bf 2}, 751 (2012)]. We present results on this model and its scaling behavior at the percolation threshold.

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• Recent advances and open challenges in percolation