Cluster Monte Carlo distributions in fractal dimensions between two and three: Scaling properties and dynamical aspects for the Ising model

[[abstract]]We study the Wolff cluster size distributions obtained from Monte Carlo simulations of the Ising phase transition on Sierpinski fractals with Hausdorff dimensions D-f between 2 and 3. These distributions are shown to be invariant when going from an iteration step of the fractal to the next under a scaling of the cluster sizes involving the exponent (beta/nu)+(gamma/nu). Moreover, the decay of the autocorrelation functions at the critical points enables us to calculate the Wolff dynamical critical exponents z for three different values of D-f. The Wolff algorithm is more efficient in reducing the critical slowing down when D-f is lowered.[[fileno]]2060113010007[[department]]工程與系統科學