Abstract
The density of states and various characteristic lengths of one-dimensional tight-binding models and disordered harmonic chains are calculated in the limit of weak disorder at the band edge of the ordered system. The density of states and a localization length of the one-dimensional Anderson model were already calculated by Derrida and Gardner; we recover their results. For the tight-binding models with off-diagonal disorder our results are in agreement with numerical calculations of Krey.
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Mielke, A., Wegner, F. Scaling behavior of one-dimensional weakly disordered models. Z. Physik B - Condensed Matter 62, 1–8 (1985). https://doi.org/10.1007/BF01303729
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DOI: https://doi.org/10.1007/BF01303729