Abstract
We analyze the density of states and some aspects of the replica method for Anderson's tight binding model on a lattice of arbitrary dimension, with diagonal disorder. We give heuristic arguments for the conjectures that the classical value of the exponent ν of the localization length is 1/2 and that the upper critical dimension,d locc , is bounded by 4≦d locc ≦6.
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Work supported in part by NSF Grant No. DMR 8100 417.
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Constantinescu, F., Fröhlich, J. & Spencer, T. Analyticity of the density of states and replica method for random schrödinger operators on a lattice. J Stat Phys 34, 571–596 (1984). https://doi.org/10.1007/BF01018559
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DOI: https://doi.org/10.1007/BF01018559