Critical behavior of the ferromagnetic Ising model on a Sierpinski carpet: Monte Carlo renormalization group study

We perform a Monte Carlo renormalization group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpinski fractal with Hausdorff dimension d(f)similar or equal to1.8928. This method is shown to be relevant to the calculation of the critical temperature T-c and the magnetic eigenexponent y(h) on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigenexponent y(t). At last, the results are shown to be consistent with a finite-size scaling analysis.