Abstract
We study a variant of the two-dimensional (2D) Anderson model of localization in which the disorder is represented by randomly chosen hopping terms. The density of states reveals an abnormally strong peak in the band center and an analysis of multifractal properties indicates that localization is less strong at E = 0 than at E ≠ 0. A finite-size-scaling analysis of localization lengths as obtained from the transfer-matrix method, shows that the state at E = 0 exhibits critical behavior up to a strip width M = 180. However, states outside the band center are localized and the critical state vanishes already for very small amounts of onsite potential disorder. Thus, there is no violation of the scaling theory of localization.
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