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

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

2005-10-17

arxiv.org/abs/cond-mat/0510442v2

Phys. Rev. Lett. 96, 165901 (2006)

Physics

Condensed Matter

Soft Condensed Matter

extended introduction, minor changes in Fig. 2b and one reference added

Scientific paper

10.1103/PhysRevLett.96.165901

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.

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