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 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.





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Hu, Yi, and Patrick Charbonneau (2021). Percolation thresholds on high-dimensional D_{n} and E_{8}-related lattices. Physical review. E, 103(6-1). p. 062115. 10.1103/physreve.103.062115 Retrieved from

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Patrick Charbonneau

Professor of Chemistry

Professor Charbonneau studies soft matter. His work combines theory and simulation to understand the glass problem, protein crystallization, microphase formation, and colloidal assembly in external fields.

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