Abstract
We analytically study bond percolation on hyperbolic lattices obtained by tiling a hyperbolic plane with constant negative Gaussian curvature. The quantity of our main concern is p(c2), the value of occupation probability where a unique unbounded cluster begins to emerge. By applying the substitution method to known bounds of the order-5 pentagonal tiling, we show that p(c2) ≥ 0.382508 for the order-5 square tiling, p(c2) ≥ 0.472043 for its dual, and p(c2)≥ 0.275768 for the order-5-4 rhombille tiling.
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