# Critical surfaces for general inhomogeneous bond percolation problems

@article{Scullard2009CriticalSF, title={Critical surfaces for general inhomogeneous bond percolation problems}, author={Christian R Scullard and Robert M. Ziff}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2009}, volume={2010}, pages={P03021} }

We present a method of general applicability for finding exact values or accurate approximations of bond percolation thresholds for a wide class of lattices. To every lattice we systematically associate a polynomial, the root of which in [0, 1] is the conjectured critical point. The method makes the correct prediction for every exactly solved problem, and comparison with numerical results shows that it is very close, but not exact, for many others. We focus primarily on the Archimedean lattices…

## 16 Citations

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- 2011

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (34, 6) lattices using the linearity approximation described in Scullard and Ziff (2010 J.…

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