One-Parameter Scaling of Localization Length and Conductance in Disordered Systems

The localization length for disordered systems is calculated with a new recursive method. The scaling behavior of the conductance is determined. The assumptions about the $\beta$ function made in recent analytical work are confirmed. Only localized states are found for two dimensions. In three dimensions there is an Anderson transition at a critical disorder of $W_c=16\mathrm{}\pm 0.5$ with critical exponents for the conductivity and the localization length of $s=\nu =1.2\mathrm{}\pm 0.3$, respectively.