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arXiv · 1407.8163

Percolation crossing probabilities in hexagons: a numerical study

Steven M. Flores·Robert M. Ziff·Jacob J. H. Simmons
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Abstract

In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these predictions with high-precision computer simulations. 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.

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Steven M. Flores, Robert M. Ziff, Jacob J. H. Simmons. 2014-07-30. Percolation crossing probabilities in hexagons: a numerical study. https://doi.org/10.1088/1751-8113%2F48%2F2%2F025001

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