Distribution of fractal clusters and scaling in the Ising model

The distribution of clusters of aligned spins in the Ising model in two and three dimensions is evaluated by Monte Carlo simulations below the critical temperature. These clusters are found to be fractals and the distribution for large-size clusters satisfies scaling properties. The scaling exponents for the distribution function, the surface exponent, and the fractal dimension of the clusters are evaluated and related to the critical exponents of the Ising model.