  We study the flow of the renormalized model parameters obtained from a
sequence of simple transformations of the 1D Anderson model with long-range
hierarchical hopping. Combining numerical results with a perturbative approach
for the flow equations, we identify three qualitatively different regimes at
weak disorder. For a sufficiently fast decay of the hopping energy, the Cauchy
distribution is the only stable fixed-point of the flow equations, whereas for
sufficiently slowly decaying hopping energy the renormalized parameters flow to
a delta peak fixed-point distribution. In an intermediate range of the hopping
decay, both fixed-point distributions are stable and the stationary solution is
determined by the initial configuration of the random parameters. We present
results for the critical decay of the hopping energy separating the different
regimes.
