Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.