Magnetic critical behavior of fractals in dimensions between 2 and 3

We report the critical exponent values of the Ising model, nu (-1), gamma/n u, and beta/nu, and the critical temperatures of three Sierpinski fractals with Hausdorff dimensions d(f) equal to 2.966, 2.904, and 2.631. The result s are calculated from finite-size scaling analysis by Monte Carlo simulatio ns. They are precise enough to show that the hyperscaling relation d(f)=2 b eta/nu+gamma/nu is satisfied. Furthermore, the discrepancy between the valu es provided by epsilon expansions and by Monte Carlo simulations shows that the critical behavior of fractals cannot be fully understood in the framew ork of strong universality.