Abstract
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 root lattices in dimensions as well as -related lattices. Here, we consider the percolation problem on for to 13 and on relatives for 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 lattices. As expected, the bond percolation threshold rapidly approaches the Bethe lattice limit as 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.
- Received 22 February 2021
- Accepted 28 May 2021
DOI:https://doi.org/10.1103/PhysRevE.103.062115
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