Publications [#357297] of Patrick Charbonneau

Papers Published

1. Hu, Y; Charbonneau, P, Percolation thresholds on high-dimensional D_{n} and E_{8}-related lattices., Physical review. E, vol. 103 no. 6-1 (June, 2021), pp. 062115 [doi]
   (last updated on 2024/04/24)

   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 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.