Direct evidence for weak universality on fractal structures

We provide a direct quantitative evidence that the critical behavior of the Ising model on self-similar lattices depends upon the geometrical features of the underlying structure. Intensive Monte Carlo simulations enable to show that the values of the ratio of exponents γ/ν depend upon the lacunarity of the structure, which measures the deviation from the translational symmetry. Finally, the topological character of the scaling corrections when the fractal dimension is smaller than 2 is discussed.