Thresholds On 3D Lattices
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold | Dimer Percolation Threshold | |||
|---|---|---|---|---|---|---|---|
| (8,3)-a | 3 | 3 | 0.577962(33) | 0.555700(22) | |||
| (10,3)-a | 3 | 3 | 0.571404(40) | 0.551060(37) | |||
| (10,3)-b | 3 | 3 | 0.565442(40) | 0.546694(33) | |||
| ice | 4 | 4 | 0.433(11) | 0.388(10) | |||
| diamond | 4 | 4 | 0.426(+0.08,-0.02) 0.4301(4) | 0.390(11), 0.3893(2) | |||
| simple cubic | 6 | 6 | 0.3116077(2), 0.311604(6), 0.311605(5), 0.311600(5), 0.3116077(4), 0.3116081(13), 0.3116080(4), 0.3116004(35) | 0.24881182(10), 0.2488125(25),
0.2488126(5) |
0.2555(1) | ||
| Icosahedral Penrose | 6 | 0.285 | 0.225 | ||||
| Penrose w/2 diagonals | 6.764 | 0.271 | 0.207 | ||||
| Stacked triangular / simple hexagonal | 8 | 8 | 0.26240(5), 0.2625(2), 0.2623(2) | 0.18602(2), 0.1859(2) | |||
| bcc | 8 | 8 | 0.2459615(10), 0.2460(3), 0.2464(7) | 0.1802875(10) | |||
| simple cubic with 3NN | 8 | 8 | 0.2455(1) | ||||
| fcc | 12 | 12 | 0.1992365(10) | 0.1201635(10) | |||
| hcp | 12 | 12 | 0.1992555(10) | 0.1201640(10) | |||
| La2-x Srx Cu O4 | 12 | 12 | 0.19927(2) | ||||
| simple cubic with 2NN | 12 | 12 | 0.1991(1) | ||||
| Penrose w/8 diagonals | 12.764 | 0.188 | 0.111 | ||||
| simple cubic with NN+3NN | 14 | 14 | 0.1420(1) | ||||
| simple cubic with NN+2NN | 18 | 18 | 0.1372(1), 0.13735(5) | ||||
| simple cubic with short-length correlation | 6+ | 6+ | 0.126(1) | ||||
| simple cubic with 2NN+3NN | 20 | 20 | 0.1036(1) | ||||
| simple cubic with NN+2NN+3NN | 26 | 26 | 0.0976(1), 0.0976445(10) |
NN = nearest neighbor, 2NN = next-nearest neighbor, 3NN = next-next-nearest neighbor
Question: the bond thresholds for the HCP and FCC lattice agree within the small statistical error. Are they identical, and if not, how far apart are they? Which threshold is expected to be bigger?
Read more about this topic: Percolation Threshold