Renormalization group approach to the multi-component site percolation on Sierpinski carpets

The multi-component site percolation problems on a family of Sierpinski carpets (SCs) are solved by the real-space renormalization group (RG) method. Three sorts of sites on an SC lattice are distinguished and three independent kinds of occupation probabilities are assigned to them. We develope the usual choice of a cell on the translationally invariant lattices and choose suitable cells to construct the RG transformation scheme based on the connectivity. The non-trivial percolation threshold values and correlation length exponents on such fractals are obtained.