Critical surfaces for general bond percolation problems

Abstract

We present a general method for predicting bond percolation thresholds and critical surfaces for a broad class of two-dimensional periodic lattices, reproducing many known exact results and providing excellent approximations for several unsolved lattices. For the checkerboard and inhomogeneous bow-tie lattices, the method yields predictions that agree with numerical measurements to more than six figures, and are possibly exact.

References in corpus (7)

• Universal Formulae for Percolation Thresholds
• Exact bond percolation thresholds in two dimensions
• Determination of the bond percolation threshold for the Kagome lattice
• Topological estimation of percolation thresholds
• Estimation of Bond Percolation Thresholds on the Archimedean Lattices
• Rigorous confidence intervals for critical probabilities
• Random Cluster Models on the Triangular Lattice

Cited by in corpus (24)

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• Universal condition for critical percolation thresholds of kagome-like lattices
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• Critical polynomials in the nonplanar and continuum percolation models
• Critical surfaces for general inhomogeneous bond percolation problems
• Bond percolation thresholds on Archimedean lattices from critical polynomial roots
• The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices
• Different thresholds of bond percolation in scale-free networks with identical degree sequence
• Percolation in Networks with Voids and Bottlenecks
• Polynomial sequences for bond percolation critical thresholds
• The percolation critical polynomial as a graph invariant
• Duality analysis on random planar lattice
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Phase diagram of the triangular-lattice Potts antiferromagnet
• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Exact solution of bond percolation on small arbitrary graphs
• Duality with real-space renormalization and its application to bond percolation
• Percolation thresholds on high dimensional $D_n$ and dense packing lattices
• The computation of generalized percolation critical polynomials by the deletion-contraction algorithm
• Percolation thresholds of randomly rotating patchy particles on Archimedean lattices
• Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices
• Some Exact Results on Bond Percolation
• Critical points of the random cluster model with Newman-Ziff sampling