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

Abstract

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.