RENORMALIZATION-GROUP APPROACH TO THE BOND PERCOLATION ON SIERPINSKI CARPETS

The critical behaviors of bond percolation on a family of Sierpinski c arpets (SCs) are studied. We distinguish two sorts of bonds and assign them to two kinds of occupation probabilities. We develop the usual c hoice of cell on translationally invariant lattices and choose suitabl e cells to cover the fractal lattice. On this basis we construct a new real-space renormalization group (RG) transformation scheme and use i t to solve the percolation problems. Phase transitions of percolation on such fractals with infinite order of ramification are found at non- trivial bond occupation probabilities. The percolation threshold value s, correlation length exponents nu, and the RG flow diagrams are obtai ned. The how diagrams are remarkably similar to those of Ising model a nd Potts model. This agrees with the correspondence between the pure b ond percolation and Potts model.