Determination of the bond percolation threshold for the Kagome lattice
Robert M. Ziff, Paul N. Suding (Department of Chemical Engineering,, University of Michigan, Ann Arbor, MI)
TL;DR
This paper accurately determines the bond percolation threshold for the Kagome lattice using the hull-gradient method, providing a precise value that challenges previous conjectures.
Contribution
It introduces a novel application of the hull-gradient method to the Kagome lattice, yielding a more accurate percolation threshold.
Findings
Percolation threshold pc = 0.5244053(3)
Results differ from earlier conjectured values
Method applicable to similar lattice systems
Abstract
The hull-gradient method is used to determine the critical threshold for bond percolation on the two-dimensional Kagome lattice (and its dual, the dice lattice). For this system, the hull walk is represented as a self-avoiding trail, or mirror-model trajectory, on the (3,4,6,4)-Archimedean tiling lattice. The result pc = 0.524 405 3(3) (one standard deviation of error) is not consistent with the previously conjectured values.
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