Cluster-size heterogeneity in the two-dimensional Ising model

TL;DR

This study numerically analyzes the heterogeneity of cluster sizes in the 2D Ising model, confirming a recently proposed scaling form and highlighting finite-size effects related to cluster geometry.

Contribution

It verifies the scaling form of cluster-size heterogeneity in the 2D Ising model and confirms the consistency of scaling exponents with theoretical values.

Findings

Scaling exponents match theoretical fractal and Fisher exponents.

Finite-size effects are significant due to cluster geometry.

Scaling form is validated in the Ising model context.

Abstract

We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension $d_f$ and the Fisher exponent $\tau$ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.