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

Felix Höfling, Thomas Franosch, and Erwin Frey
Phys. Rev. Lett. 96, 165901 – Published 24 April 2006

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 and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.

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  • Received 17 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.165901

©2006 American Physical Society

Authors & Affiliations

Felix Höfling1, Thomas Franosch1,2, and Erwin Frey2

  • 1Hahn-Meitner-Institut Berlin, Abteilung Theorie, Glienicker Straße 100, D-14109 Berlin, Germany
  • 2Arnold Sommerfeld Center and CeNS, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany

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Issue

Vol. 96, Iss. 16 — 28 April 2006

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