Geodesic
A disproof of Tsallis' bond percolation threshold conjecture for the Kagome lattice
John C. Wierman1 ; Gaoran Yu1 ; Theodore Huang1
1Johns Hopkins University
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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In 1982, Tsallis derived a formula which proposed an exact value of 0.522372078... for the bond percolation threshold of the kagome lattice. We use the substitution method, which is based on stochastic ordering, to compare the probability distribution of connections in the homogeneous bond percolation model on the kagome lattice to those of an exactly-solved inhomogeneous bond percolation model on the martini lattice. The bounds obtained are $0.522394, where the lower bound shows that the value conjectured by Tsallis is incorrect.
DOI : 10.37236/5117
Classification : 82B43, 05C80, 60K35
Mots-clés : percolation theory, set partition, stochastic ordering

John C. Wierman  1   ; Gaoran Yu  1   ; Theodore Huang  1

1 Johns Hopkins University 
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John C. Wierman; Gaoran Yu; Theodore Huang. A disproof of Tsallis' bond percolation threshold conjecture for the Kagome lattice. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/5117

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