Monte Carlo simulation of an Ising model on a Sierpinski carpet

We study by Monte Carlo simulation the equilibrium and dynamical critical properties of fractal lattices with noninteger Hausdorff dimension. These lattices are known to be good candidates to bridge the gap between integer dimensions. Focusing on the Sierpinski carpet with Ising spins, we are able to obtain the critical exponents that are to be compared to the predictions of the renormalization group. We point out that the use of finite-size scaling is forbidden for fractal lattices. This might explain the difference from the exponents obtained in previous studies.