Abstract
We report the critical exponent values of the Ising model, ν -1 , γ/ν, and β/ν, and the critical temperatures of three Sierpínski fractals with Hausdorff dimensions d f 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 d f = 2β/ν+ γ/ν is satisfied. Furthermore, the discrepancy between the values provided by ∈ expansions and by Monte Carlo simulations shows that the critical behavior of fractals cannot be fully understood in the framework of strong universality.