Spectral singularities and localisation in one- and quasi-one-dimensional systems with off-diagonal disorder

The author presents a numerical method for calculating the integrated density of states and the localisation length in quasi-one-dimensional tight-binding disordered systems. The results for the one-dimensional Anderson model with off-diagonal disorder confirm that the singularities for the density of states and the localisation length are in the form predicted by Dyson. In two dimensions the singularity for the density of states near E=0 approaches the form rho (E) varies as E - phi for weak off-diagonal disorder. The author obtained approximately 1 / 3 for the exponent phi consistent with current fractal viewpoints. Some results for strong off-diagonal disorder in two dimensions where the singularity is of a different nature are also presented.