# 渗流理论

## 渗流阈值

d 配位数z 点渗流 边渗流
2 4 0.59274601(2)[4] 1/2
3 6 0.3116077(4)[5] 0.2488126(5)[6]
4 8 0.1968861(14),[7]0.19688561(3)[8] 0.1601314(13),[7] 0.16013122(6)[8]
5 10 0.1407966(15),[7] 0.14079633(4)[8] 0.118172(1),[7] 0.11817145(3)[8]
6 12 0.109017(2),[7] 0.109016661(8)[8] 0.0942019(6),[7] 0.09420165(2)[8]
7 14 0.0889511(9), [7] 0.088951121(1),[8] 0.0786752(3),[7] 0.078675230(2)[8]
8 16 0.0752101(5),[7] 0.075210128(1)[8] 0.06770839(7),[7] 0.0677084181(3)[8]
9 18 0.0652095(3),[7] 0.0652095348(6)[8] 0.05949601(5),[7] 0.0594960034(1)[8]
10 20 0.0575930(1),[7] 0.0575929488(4)[8] 0.05309258(4),[7] 0.0530925842(2)[8]
11 22 0.05158971(8),[7] 0.0515896843(2)[8] 0.04794969(1),[7] 0.04794968373(8)[8]
12 24 0.04673099(6),[7] 0.0467309755(1)[8] 0.04372386(1),[7] 0.04372385825(10)[8]
13 26 0.04271508(8),[7] 0.04271507960(10)[8] 0.04018762(1),[7] 0.04018761703(6)[8]

## 渗流临界指数

${\displaystyle \tau ={\frac {d}{d_{\text{f}}}}+1\,\!}$
${\displaystyle \eta =2+d-2d_{\text{f}}\,\!}$

## 参考资料

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2. ^ Dietrich Stauffer; Ammon Aharony. Introduction to percolation theory revised second edition. CRC press. 2014. ISBN 0748400273.
3. ^ Bollobás, Béla; Riordan, Oliver. Sharp thresholds and percolation in the plane. Random Structures and Algorithms. 2006, 29 (4): 524–548. ISSN 1042-9832. . doi:10.1002/rsa.20134.
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7. Grassberger, Peter. Critical percolation in high dimensions. Physical Review E. 2003, 67 (3): 4. Bibcode:2003PhRvE..67c6101G. . doi:10.1103/PhysRevE.67.036101.
8. Mertens, Stephan; Christopher Moore. Percolation Thresholds and Fisher Exponents in Hypercubic Lattices. 2018. [cond-mat.stat-mech].