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2024 | OriginalPaper | Chapter

A New Upper Bound for the Site Percolation Threshold of the Square Lattice

Authors : John C. Wierman, Samuel P. Oberly

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

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Abstract

The upper bound for the site percolation threshold of the square lattice is reduced from 0.679492 to 0.666894, providing the first improvement since 1995. The bound is obtained by using the substitution method with new computational reductions which make calculations for site models more efficient. The substitution method is applied, comparing the site percolation model on a self-matching lattice to the square lattice site percolation model in a two-stage process.

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previous chapter The Existence of a Knight’s Tour on the Surface of Rectangular Boxes
next chapter Prime, Composite and Fundamental Kirchhoff Graphs
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Metadata
Title
A New Upper Bound for the Site Percolation Threshold of the Square Lattice
Authors
John C. Wierman
Samuel P. Oberly
Copyright Year
2024
Book
Combinatorics, Graph Theory and Computing

Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-62166-6_9

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