[21] Monte Carlo Simulation of a Ising Model on a Sierpinski Carpet

We study by Monte Carlo simulation the equilibrium and dynamical critical properties of fractal lattices with non-integer 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 which 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 to the exponents obtained in previous studies.