Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

Details Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

1996-06-05

arxiv.org/abs/cond-mat/9606021v2

Europhys. Lett. 34 (1996) 587

Physics

Condensed Matter

4 pages in revtex, 3 postscript figures

Scientific paper

10.1209/epl/i1996-00499-9

We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a crossover between Wigner and Poisson distributions. We perform a self-contained finite-size scaling analysis to find a single-valued one-parameter function $\gamma (L/\xi)$ which governs the crossover. The scaling parameter $\xi(W)$ is deduced and compared with the localization length. $\gamma ( L/\xi)$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.

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