• DOI:10.1103/PhysRevE.103.062115
• Corpus ID: 231979212

Percolation thresholds on high-dimensional D_{n} and E_{8}-related lattices.

@article{Hu2021PercolationTO,
  title={Percolation thresholds on high-dimensional D\_\{n\} and E\_\{8\}-related lattices.},
  author={Yi Hu and Patrick Charbonneau},
  journal={Physical review. E},
  year={2021},
  volume={103 6-1},
  pages={
          062115
        }
}

• Yi Hu, P. Charbonneau
• Published 18 February 2021
• Computer Science
• Physical review. E

The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now also facilitates the study of D_{n} root lattices in n dimensions as well as E_{8}-related lattices. Here, we consider the percolation problem on D_{n} for n=3 to 13 and on E_{8} relatives for n=6 to 9. Precise estimates for both site and bond percolation thresholds obtained from invasion percolation simulations are compared with dimensional series expansion based on lattice animal enumeration for D_{n} lattices. As expected, the bond percolation threshold rapidly approaches the Bethe lattice limit as n increases for these high-connectivity lattices. Corrections, however, exhibit clear yet unexplained trends. Interestingly, the finite-size scaling exponent for invasion percolation is found to be lattice and percolation-type specific.