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 yh associated with one of the eigendirection 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. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003.