Thresholds For Directed Percolation
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold |
|---|---|---|---|
| (1+1)-d square, diagonal direction | 2 | 0.705489(4), 0.70548522(4) | 0.644701(2), 0.644701(1), 0.64470015(5), 0.644700185(5) |
| (1+1)-d triangular | 3 | 0.5956468(5) | 0.478025(1) |
| (2+1)-d simple cubic, diagonal planes | 3 | 0.43531(1) | 0.382223(7) |
| (2+1)-d square nn (= bcc) | 4 | 0.3445736(3), 0.344575(15) | 0.2873383(1), 0.287338(3) |
| (3+1)-d hypercubic, diagonal planes | 4 | 0.3025(10) | |
| (3+1)-d cubic, nn | 6 | 0.2081040(4) | 0.1774970(5) |
| (3+1)-d body-centered hypercubic | 8 | 0.160950(30) | |
| (4+1)-d hypercubic, nn | 8 | 0.1461593(2), 0.1461582(3) | 0.1288557(5) |
| (4+1)-d body-centered hypercubic | 16 | 0.075582(17)
0.0755850(3) |
|
| (5+1)-d hypercubic, nn | 10 | 0.1123373(2) | 0.1016796(5) |
| (5+1)-d body-centered hypercubic | 32 | 0.035967(23) | |
| (6+1)-d hypercubic, nn | 12 | 0.0913087(2) | 0.0841997(14) |
| (7+1)-d hypercubic,nn | 14 | 0.07699336(7) | 0.07195(5) |
nn = nearest neighbors. For a (d+1)-dimensional hypercubic system, the hypercube is in d dimensions and the time direction points to the 2D nearest neighbors.
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