Abstract
The density of states and inverse participation ratios have been obtained numerically by directly diagonalising the tight-binding Hamiltonian on the square and cubic lattices with Gaussian randomness in the off-diagonal elements. The density of states, which has a singularity at the band centre, is well approximated in both dimensions by the loop expansion of Oppermann and Wegner (1979) taken to one-loop order. All the eigenvectors appear to be localised in two dimensions.
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