Fractals and interpolating dimensions

We describe a computer study of Ising models on a generalization of Sierpinsky carpets of Hausdorf dimension between one and four. We measure the critical coupling and the exponent γ as a function of dimension. We also show how finite size scaling analyses can be done using fractals. Our results strongly suggest that fractals of the Sierpinsky carpet type can be used to interpolate between integer dimensions to study the critical behavior of statistical systems. (orig.)