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

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  • 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. ... [Read More]

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60 files (402 KB)
Data Citation
  • Hu, Y., & Charbonneau, P. (2021). Data and scripts from: Percolation thresholds on high-dimensional D_n and E_8-related lattices. Duke Research Data Repository. https://doi.org/10.7924/r4fx7bk95
DOI
  • 10.7924/r4fx7bk95
Publication Date
ARK
  • ark:/87924/r4fx7bk95
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Funding Agency
  • Simons Foundation
Grant Number
  • 454937
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Title
  • Data and scripts from: Percolation thresholds on high-dimensional D_n and E_8-related lattices

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