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 $\ensuremath{\beta}$ 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 ${W}_{c}=16\ifmmode\pm\else\textpm\fi{}0.5$ with critical exponents for the conductivity and the localization length of $s=\ensuremath{\nu}=1.2\ifmmode\pm\else\textpm\fi{}0.3$, respectively.