Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study
Abstract
We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with Hausdorff dimension df 1.8928. This method is shown to be relevant to the calculation of the critical temperature Tc and the magnetic eigen-exponent yh on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent yt. At last, the results are shown to be consistent with a finite size scaling analysis.
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