  The single-parameter scaling hypothesis predicts the absence of delocalized
states for noninteracting quasiparticles in low-dimensional disordered systems.
We show analytically and numerically that extended states may occur in the one-
and two-dimensional Anderson model with a nonrandom hopping falling off as some
power of the distance between sites. The different size scaling of the bare
level spacing and the renormalized magnitude of the disorder seen by the
quasiparticles finally results in the delocalization of states at one of the
band edges of the quasiparticle energy spectrum. The delocalized nature of
those eigenstates is investigated by numerical diagonalization of the
Hamiltonian and by the supersymmetric method for disorder averaging, combined
with a renormalization group analysis.
