We investigate the effects of impurities and changing ring geometry on the
energetics of quantum rings under different magnetic field strengths. We show
that as the magnetic field and/or the electron number are/is increased, both
the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become
insensitive to whether the ring is circular or square in shape. This is in
qualitative agreement with experiments. However, we also find that the
Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities
and can be completely obliterated by a high level of impurity density. In the
many-electron calculations we use a recently developed fourth-order imaginary
time projection algorithm that can exactly compute the density matrix of a
free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR