K. J. Schrenk, N. A. M. Araujo, H. J. Herrmann
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 ${p_c^\text{bond}=0.186\;02\pm0.000\;02}$ for bonds and ${p_c^\text{site}=0.262\;40\pm0.000\;05}$ for sites. The number of clusters at the threshold per site is ${n_c^\text{bond}=0.284\;58\pm0.000\;05}$ and ${n_c^\text{site}=0.039\;98\pm0.000\;05}$. The stacked triangular lattice is a natural choice to simulate the sharing of underground reservoirs [Sci. Rep. {\bf 2}, 751 (2012)]. We present results on the reservoir sharing model and its scaling behavior at the percolation threshold.
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http://arxiv.org/abs/1302.0484
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