Bounds of percolation thresholds on hyperbolic lattices.
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.
School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Junghoon F
JF
Lee
Seung Ki
SK
Baek