Statistical description of magnetic domains in the Ising model

TL;DR

This paper analyzes the statistical properties of magnetic domains in the Ising model near phase transition, revealing a Pareto distribution of domain sizes using Mandelbrot-Zipf power law.

Contribution

It introduces a novel application of Mandelbrot-Zipf power law to describe inhomogeneity and domain size distribution in the Ising model at criticality.

Findings

Domain size distribution follows Pareto law near critical temperature

Mandelbrot-Zipf power law effectively characterizes inhomogeneity

Statistical description enhances understanding of phase transition phenomena

Abstract

We use the Mandelbrot-Zipfs power law for the description of the inhomogenity of the spin system. We describe the statistical distributions of the domain's masses in the Ising model near the phase transition induced by the temperature. The statistical distribution near the critical point appears to be of the Pareto type.