Critical Percolation in High Dimensions
摘要
We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing which allowed us to simulate clusters of millions of sites on computers with less than 500 MB memory; (ii) a histogram method which allowed us to obtain information for several p values from a single simulation; and (iii) a new variance reduction technique which is especially efficient at high dimensions where it reduces error bars by a factor up to approximately 30 and more. Based on these data we propose a new scaling law for finite cluster size corrections.
引用
@article{arxiv.cond-mat/0202144,
title = {Critical Percolation in High Dimensions},
author = {Peter Grassberger},
journal= {arXiv preprint arXiv:cond-mat/0202144},
year = {2009}
}
备注
5 pages including figures, RevTeX