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We study the flow of the renormalized model parameters obtained from asequence of simple transformations of the 1D Anderson model with long-rangehierarchical hopping. Combining numerical results with a perturbative approachfor the flow equations, we identify three qualitatively different regimes atweak disorder. For a sufficiently fast decay of the hopping energy, the Cauchydistribution is the only stable fixed-point of the flow equations, whereas forsufficiently slowly decaying hopping energy the renormalized parameters flow toa delta peak fixed-point distribution. In an intermediate range of the hoppingdecay, both fixed-point distributions are stable and the stationary solution isdetermined by the initial configuration of the random parameters. We presentresults for the critical decay of the hopping energy separating the differentregimes.

The renormalization flow of the hierarchical Anderson model at weak disorder