Stacked triangular lattice: Percolation properties

TL;DR

This study investigates the percolation properties of the stacked triangular lattice using Monte Carlo simulations, providing precise thresholds and cluster counts, and explores the RGB model's behavior at criticality.

Contribution

It offers the first detailed analysis of percolation thresholds and cluster properties on the stacked triangular lattice, including insights into the RGB model at the percolation threshold.

Findings

Percolation threshold for bonds: 0.18602 ± 0.00002

Percolation threshold for sites: 0.26240 ± 0.00005

Cluster count per site at threshold: 0.28458 ± 0.00005

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 $p_c^\text{bond}=0.186\;02\pm0.000\;02$ 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 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.