  Magnetization processes of the spin-1/2 antiferromagnetic $XXZ$ model in two
and three spatial dimensions are studied using quantum Monte Carlo method based
on stochastic series expansions. Recently developed operator-loop algorithm
enables us to show a clear evidence of the first-order phase transition in the
presence of an external magnetic field. Phase diagrams of closely related
systems, hard core bosons with nearest-neighbor repulsions, are also discussed
focusing on possibilities of phase-separated and supersolid phases.
