New critical frontiers for the Potts and percolation models

Abstract

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.

9 pages, 5 figures

References in corpus (3)

• Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations
• Random Cluster Models on the Triangular Lattice
• Generalized cell/dual-cell transformation for percolation, and new exact thresholds

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• Percolation on Hypergraphs with Four-Edges
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• Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices
• Exact critical points of the O($n$) loop model on the martini and the 3-12 lattices
• Self-dual planar hypergraphs and exact bond percolation thresholds
• Percolation in the two-dimensional Ising model