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Universality and RSW for inhomogeneous bond percolation

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The star-triangle transformation is used to obtain an equivalence extending over the set of some (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are box-crossing (RSW) inequalities and the universality of alternating arms exponents (assuming they exist) for such models. The models’ parameter-values are those at which the transformation is valid. This is a step towards proving the universality and conformality of these processes. It implies criticality of such values, thereby providing a new proof of the critical point of inhomogeneous systems. The proofs extend to certain isoradial models to which previous methods do not apply.

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