Matrix continued-fraction calculation of localization length in disordered systems

A Matrix Continued-Fraction method is used to study the localization length of the states at the band center of a two dimensional crystals with disorder given by the Anderson model. It is found that exponentially localized states which scale according to the work of Mac Kinnon and Kramer, becomes weakly localized as the disorder becomes weaker, and there is some critical disorder for which the localization length does not saturate with the width of the strips, this confirms the resuts found by Pichard and Sarma. Weakly localized states are also found in one dimension for w/v <or approx., 1. The transition from extended to localized states is also examined in one dimension. (author)