Effects of boundary conditions on the critical spanning probability

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 $p_c=0.311605(5)$ in the cubic lattice.

8 pages Latex, To appear in Int. J. Mod. Phys. C

Cited by in corpus (8)

• Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
• Simple cubic random-site percolation thresholds for complex neighbourhoods
• Percolation of disordered jammed sphere packings
• Correction-to-scaling exponent for two-dimensional percolation
• Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
• Percolation in three-dimensional random field Ising magnets
• Universality class for bootstrap percolation with $m=3$ on the cubic lattice
• Percolation of sites not removed by a random walker in $d$ dimensions