Exact results of Potts model on a special kind of Sierpinski carpets

With a way different from renormalization group method and graph theory [1, 2], we have calculated the exact partition function, free energy and spin-spin correlation function of Potts model, other than the Ising model, on a special Sierpinski Carpet (SC). The results indicate no phase transition occurs at any finite temperature for the fractal with finite R(the order of ramification) and thus consist with the conclusion produced by renormalization group method and other physical arguments.