Effects of boundary conditions on the critical spanning probability
Muktish Acharyya & Dietrich Stauffer (Cologne University, Germany)
TL;DR
This paper investigates how boundary conditions influence the probability of spanning clusters at the percolation threshold through simulations in 2D and 3D lattices, also providing a precise estimate of the critical probability in 3D.
Contribution
It systematically studies the effect of boundary conditions on spanning probabilities and reports a new accurate value for the 3D cubic lattice percolation threshold.
Findings
Boundary conditions significantly affect spanning probabilities.
Estimated critical percolation threshold in 3D cubic lattice: p_c = 0.311605(5).
Spanning probabilities vary with boundary conditions in 2D and 3D simulations.
Abstract
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find in the cubic lattice.
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