Percolation Thresholds and Fisher Exponents in Hypercubic Lattices
Statistical Mechanics
2018-08-29 v3
Abstract
We use invasion percolation to compute highly-accurate numerical values for bond and site percolation thresholds p_c on the hypercubic lattice Z^d for d = 4,,,,,13. We also compute the Fisher exponent tau governing the cluster size distribution at criticality. Our results support the claim that the mean-field value tau = 5/2 holds for d >= 6, with logarithmic corrections to power-law scaling at d=6.
Keywords
Cite
@article{arxiv.1806.08067,
title = {Percolation Thresholds and Fisher Exponents in Hypercubic Lattices},
author = {Stephan Mertens and Cristopher Moore},
journal= {arXiv preprint arXiv:1806.08067},
year = {2018}
}