Empirical formula for site and bond percolation thresholds on Archimedean and 2-uniform lattices

W. Lebrecht, P.M. Centres and A.J. Ramirez-Pastor

Physica A: Statistical Mechanics and its Applications, 2021, vol. 569, issue C

Abstract: The problem of percolation on Archimedean and 2-uniform lattices is investigated. An empirical formula is postulated for the ratio between the site percolation threshold pcs, and the bond percolation threshold pcb. The expression is pcs∕pcb≈az̄s3∕z̄s−12, where a=0.16428 and z̄s is the mean number of nearest neighbors of a given lattice site. For each of the 11 Archimedean and 20 2-uniform lattices which constitute our sample, a good correspondence is obtained with previous calculations of pcs∕pcb. The formula is found to be also valid for standard percolation in three-dimensional lattices and for percolation of tortuous k-mers [objects occupying k adjacent lattice elements (sites or bonds)] on square lattices.

Keywords: Percolation; Archimedean lattices; 2-uniform lattices (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:569:y:2021:i:c:s0378437121000741

DOI: 10.1016/j.physa.2021.125802

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