Percolation thresholds on high-dimensional Dn and E8-related lattices

Yi Hu and Patrick Charbonneau
Phys. Rev. E 103, 062115 – Published 11 June 2021

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 Dn root lattices in n dimensions as well as E8-related lattices. Here, we consider the percolation problem on Dn for n=3 to 13 and on E8 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 Dn 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.

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  • Received 22 February 2021
  • Accepted 28 May 2021

DOI:https://doi.org/10.1103/PhysRevE.103.062115

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Yi Hu1 and Patrick Charbonneau1,2

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
  • 2Department of Physics, Duke University, Durham, North Carolina 27708, USA

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Issue

Vol. 103, Iss. 6 — June 2021

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