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arXiv · 1806.08067

Percolation Thresholds and Fisher Exponents in Hypercubic Lattices

Stephan Mertens·Cristopher Moore
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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.

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Stephan Mertens, Cristopher Moore. 2018-08-07. Percolation Thresholds and Fisher Exponents in Hypercubic Lattices. https://doi.org/10.1103/physreve.98.022120

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