Abstract
A position space renormalization-group method, suitable for studying the localization properties of electrons in a disordered system, was developed. Two different approximations to a well defined exact procedure were used. The first method is a perturbative treatment to lowest order in the inter-cell couplings. This yields a localization edge in three dimensions, while in two dimensions no fixed point is found, indicating localization even for small randomness. The second method is an application of the finite lattice approximation, in which the inter-cell hopping between two (or more) cells is treated to infinite order in perturbation theory. This method was used in two dimensions only, yielding results that are in agreement with those of the lowest order approximation.
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Domany, E., Sarker, S. (1981). Scaling theory of Anderson localization: A renormalization group approach. In: Castellani, C., Di Castro, C., Peliti, L. (eds) Disordered Systems and Localization. Lecture Notes in Physics, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012566
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DOI: https://doi.org/10.1007/BFb0012566
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