Magnetic critical behavior of fractals in dimensions between 2 and 3

We report the critical exponent values of the Ising model, n21, g /n , and b/n , and the critical temperatures of three Sierpi'nski fractals with Hausdorff dimensions df equal to 2.966, 2.904, and 2.631. The results are calculated from finite-size scaling analysis by Monte Carlo simulations. They are precise enough to show that the hyperscaling relation df52b/n1g /n is satisfied. Furthermore, the discrepancy between the values provided by e expansions and by Monte Carlo simulations shows that the critical behavior of fractals cannot be fully understood in the framework of strong universality.