Abstract
We study the critical behavior of the three-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations for a Hausdorff dimension d f ≃ 1.8928. The phase transition is shown to be second-order. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents γ/υ. We find that the scaling corrections affect the behavior of most of the thermodynamic quantities. However, the sequence of intersection points extracted from the Binder's cumulant provides bounds for the critical temperature. We are able to give the bounds for the exponent 1/υ as well as for the ratio of the exponents β/υ, which are compatible with the results calculated from the hyperscaling relation.