Hierarchical renormalization-group study on the planar bond-percolation problem

For certain hierarchical structures, one can study the percolation problemusing the renormalization-group method in a very precise way.We show that the idea can be alsoapplied to two-dimensional planar lattices by regarding them as hierarchicalstructures. Either a lower bound or an exact critical probability can beobtained with this method and the correlation-length critical exponent isapproximately estimated as $\nu \approx 1$.