The geometrically-averaged density of states as a measure of localization

Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, ${\rho }_g(\omega )$, as an order parameter for the Anderson transition is examined. In the context of finite-size systems we examine complications which arise from finite energy resolution. Furthermore we demonstrate that even in infinite systems a decline in ${\rho }_g(\omega )$ with increasing disorder strength is not uniquely associated with localization.