Scaling and localization lengths of a topologically disordered system

TL;DR

This paper investigates a disordered system's localization properties, demonstrating it shares universal behavior with the Anderson model through numerical analysis of localization lengths across energies.

Contribution

It introduces a disordered model with random site distribution and shows it exhibits universal localization behavior similar to the Anderson model.

Findings

Localization length follows universal scaling across energies.

Model's behavior matches that of the Anderson model.

Finite-size-scaling effectively characterizes localization properties.

Abstract

We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical evidence that this model displays the same universal behavior as the standard Anderson model. We use finite-size-scaling to find the localization length as a function of energy and density, including localized states away from the delocalization transition. Results at many energies all fit onto the same universal scaling curve.