# The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices

@article{Ziff2012TheCM, title={The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices}, author={Robert M. Ziff and Christian R Scullard and John C. Wierman and M. Sedlock}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2012}, volume={45} }

We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at first to fall into any known solvable class. Although our argument is mathematically rigorous only on a region of the manifold, we conjecture that the formula is correct over its entire domain, and we provide a non-rigorous argument for this that employs the negative probability regime of the triangular lattice critical…

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