Critical Percolation in High Dimensions

Details Critical Percolation in High Dimensions Critical Percolation in High Dimensions

2002-02-08

arxiv.org/abs/cond-mat/0202144v2

Physics

Condensed Matter

Statistical Mechanics

5 pages including figures, RevTeX

Scientific paper

10.1103/PhysRevE.67.036101

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.

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