  We show that a proper consideration of the contribution of Trugman loops
leads to a fairly low effective mass for a hole moving in a square lattice
Ising antiferromagnet, if the bare hopping and the exchange energy scales are
comparable. This contradicts the general view that because of the absence of
spin fluctuations, this effective mass must be extremely large. Moreover, in
the presence of a transverse magnetic field, we show that the effective hopping
integrals acquire an unusual dependence on the magnetic field, through
Aharonov-Bohm interference, in addition to significant retardation effects. The
effect of the Aharonov-Bohm interference on the cyclotron frequency (for small
magnetic fields) and the Hofstadter butterfly (for large magnetic fields) is
analyzed.
