Data and scripts from: Percolation thresholds on high-dimensional D_n and E_8-related lattices


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 dimension 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.

Data Access

Duke Authors

Cited Authors

  • Hu, Y; Charbonneau, P

Published Date

  • June 2, 2021

Digital Object Identifier (DOI)

  • 10.7924/r4fx7bk95