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 (4)

• Exact bond percolation thresholds in two dimensions
• Topological estimation of percolation thresholds
• Estimation of Bond Percolation Thresholds on the Archimedean Lattices
• Rigorous confidence intervals for critical probabilities

Cited by in corpus (3)

• Universal condition for critical percolation thresholds of kagome-like lattices
• Different thresholds of bond percolation in scale-free networks with identical degree sequence
• Percolation in Networks with Voids and Bottlenecks