Abstract
Following the methods proposed by Yonezawa, Sakamoto and Hori, we have calculated the percolation thresholds , their error bars , and the correlation length exponents of a family of the Sierpinski carpets for the site percolation problems by making use of MonteCarlo simulations and finite size scaling. We have found the dependence of and on the fractal dimensionality and the lacunarity. We ascertain that the site percolation problems on a family of Sierpinski carpets with central cutouts and different belong to different universal classes, and those on Sierpinski carpets with same but of different lacunarities belong to different universal classes.
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