Eur. Phys. J. B 32, 81-86 (2003)
https://doi.org/10.1140/epjb/e2003-00076-8

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

¹ Laboratoire de physique théorique de la matière condensée, Pôle matière et systèmes complexes (FR2438 CNRS) , Université Paris 7, case 7020, 2 place Jussieu, 75251 Paris Cedex 05, France
² Département de physique et modélisation, Université d'Evry-Val d'Essonne, Boulevard F. Mitterrand, 91025 Evry Cedex, France

Corresponding author: ^a pmo@ccr.jussieu.fr

Received: 29 November 2002
Published online: 14 March 2003

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 between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as 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 is lowered.