超立方晶格中的渗流阈值和费舍尔指数。

Percolation thresholds and Fisher exponents in hypercubic lattices.

机构信息

Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Institut für Physik, Universität Magdeburg, Universitätsplatz 2, 39016 Magdeburg, Germany.

出版信息

Phys Rev E. 2018 Aug;98(2-1):022120. doi: 10.1103/PhysRevE.98.022120.

DOI:10.1103/PhysRevE.98.022120

PMID:30253462

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 τ governing the cluster size distribution at criticality. Our results support the claim that the mean-field value τ=5/2 holds for d≥6, with logarithmic corrections to power-law scaling at d=6.

摘要

我们使用入侵渗流来计算超立方晶格 Z^{d} 上的键和点渗流阈值 p_{c} 的高精度数值，其中 d=4,...,13。我们还计算了控制临界点上簇大小分布的 Fisher 指数 τ。我们的结果支持以下观点，即在 d≥6 时均值场值 τ=5/2 成立，而在 d=6 时有对数修正的幂律标度。