Convergence of threshold estimates for two-dimensional percolation
Abstract
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system with a square boundary, specifically for site percolation on a square lattice. We show that the convergence of the so-called "average-probability" estimate is described by a non-trivial correction-to-scaling exponent as predicted previously, and measure the value of this exponent to be 0.90(2). For the "median" and "cell-to-cell" estimates of the percolation threshold we verify that convergence does not depend on this exponent, having instead a slightly faster convergence with a trivial analytic leading exponent.
Cite
@article{arxiv.cond-mat/0203496,
title = {Convergence of threshold estimates for two-dimensional percolation},
author = {R. M. Ziff and M. E. J. Newman},
journal= {arXiv preprint arXiv:cond-mat/0203496},
year = {2009}
}
Comments
11 pages, 4 figures