Critical surfaces for general bond percolation problems

TL;DR

This paper introduces a versatile method for predicting bond percolation thresholds and critical surfaces in various 2D periodic lattices, achieving high accuracy and reproducing known results while providing new insights into unsolved cases.

Contribution

A novel general approach for estimating percolation thresholds that matches known results and offers precise predictions for previously unsolved lattice problems.

Findings

Accurately predicts thresholds for multiple lattices

Reproduces many known exact results

Provides high-precision estimates for unsolved lattices

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.