The coefficient for exponential attenuation of the averaged Green function [${\lim }_{\mathrm{\delta }\to 0}$<${\mathit{G}}_{\mathrm{OR}}$(E+iδ0${\mathrm{\gtrsim }}_{\mathrm{av}}$∼${\mathit{e}}^{\mathrm{-}\mathrm{\kappa }\mathit{R}}$] is calculated for several infinite lattices in one, two, and three dimensions with a diagonal Lorentzian disorder of site energies (Lloyd model). In the limit of extended states, l=${\kappa }^{\mathrm{-}1}$ coincidences with the phase coherence length and with the mean free path associated with ‖k〉 states.

In the opposite limit, that of strongly localized states, the inequality κ≥γ is almost satisfied as an equality where γ is the inverse localization length. Our results for κ are the same as those calculated by Johnston and Kunz who associate their results with γ, that is, with the localization length. This leads us to reinterpret their results and to conclude that, when the dimensionality is higher than 2, there is still a strong possibility of a mobility edge in this model.

• Received 24 June 1986

DOI:https://doi.org/10.1103/PhysRevB.34.8545