Cluster Monte Carlo dynamics for the Ising model on fractal structures in dimensions between one and two

摘要

We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension D_f between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent y_h associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as D_f tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculated dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when D_f is lowered.