The decimation method and Anderson localization

We discuss the application of the decimation method to the problem of Anderson localization. In one dimension, the renormalized interactions defined in this method are found to scale towards weak coupling (indicative of localized states) for all values of the strength of (diagonal) disorder. In two dimensions, the interactions appear to scale toward weak/strong coupling for low/high disorder. However the latter results remain puzzling, in that no clear connection between the scaling behaviour and the localization length has emerged