Upper Bound for Critical Probability of Site Percolation on Triangular Lattice
Mathematical Physics
2013-08-22 v1 math.MP
Computational Physics
Abstract
In site percolation, vertices (sites) of a graph are open with probability p, and there is critical p, for which open vertices form an open path the long way across a graph, so a vertex at the origin is a part of an infinite connected open vertex set. Smirnov found that for triangular lattice critical p is 0.5, but there is the traversal, from the origin upwards, so that an infinite connected open vertex set exists for critical p=0.3535.
Keywords
Cite
@article{arxiv.1308.4549,
title = {Upper Bound for Critical Probability of Site Percolation on Triangular Lattice},
author = {Marko Pujic},
journal= {arXiv preprint arXiv:1308.4549},
year = {2013}
}