Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation

TL;DR

This paper investigates the localization transition in the 3D Lorentz model using simulations, linking it to continuum percolation theory, and identifies critical behavior and scaling properties.

Contribution

It provides a quantitative explanation of the transition in the Lorentz model through continuum percolation theory, including critical densities and exponents.

Findings

Excellent match of critical density and exponents with theory

Data collapse achieved for mean-square displacements

Non-Gaussian parameter diverges at transition

Abstract

The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory, an excellent matching of both the critical density and exponents is obtained. Upon exploiting a dynamic scaling Ansatz employing two divergent length scales we find data collapse for the mean-square displacements and identify the leading-order corrections to scaling. The non-Gaussian parameter is predicted to diverge at the transition.