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

By Pascal Monceau and Pai-Yi Hsiao

Abstract

International audienceWe study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df 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 Df 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 Df is lowered

Topics: Phase transitions and critical phenomena, Fractals, Classical spin models, Numerical simulation studies, Systems obeying scaling laws, stochastic dynamics, 68.35.Rh; 05.45.Df; 75.10.Hk; 75.40.Mg; 89.75.Da, [ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
Publisher: Springer-Verlag
Year: 2003
DOI identifier: 10.1140/epjb
OAI identifier: oai:HAL:hal-00701552v1
Provided by: Hal-Diderot
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