Scaling law of Wolff cluster surface energy

TL;DR

This paper investigates the scaling behavior of Wolff cluster surface energy on fractal lattices within the Ising model, establishing new scaling relations and introducing a novel surface energy exponent linked to dynamical properties.

Contribution

It introduces a new scaling relation for Wolff cluster surface energy and defines a novel exponent connected to the cluster's surface properties.

Findings

Surface energy follows a power law with lattice size.

A new scaling relation for surface energy distribution is established.

A new exponent related to surface energy is introduced and linked to dynamical exponents.

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.