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

Abstract:

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 calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when D_f is lowered.