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Scaling law of Wolff cluster surface energy

Pai-Yi Hsiao·Pascal Monceau
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Abstract

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.

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Pai-Yi Hsiao, Pascal Monceau. 2003-04-02. Scaling law of Wolff cluster surface energy. https://doi.org/10.1103/physrevb.67.172403

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