Percolation crossing probabilities in hexagons: a numerical study

In a recent article (Simmons 2013 J. Phys. A: Math. Theor. 46 494015), the last author of this article used c = 0 logarithmic conformal field theory to predict crossing probability formulas for percolation clusters inside a hexagon with free boundary conditions. In the present article, we verify these predictions with high-precision computer simulations for equiangular hexagons with side lengths alternating from short to long. Our simulations generate percolation-cluster perimeters with hull walks on a triangular lattice inside a hexagon. Each sample comprises two hull walks, and the order in which these walks strike the bottom and upper left/right sides of the hexagon determines the crossing configuration of the percolation sample. We compare our numerical results with the predicted crossing probabilities, finding excellent agreement. (paper)