  The magnetization process of the spin-1/2 antiferromagnetic XXZ model with
Ising-like anisotropy in the ground state is investigated. We show numerically
that the Ising-like XXZ models on square and cubic lattices show a first-order
phase transition at some critical magnetic field. We estimate the value of the
critical field and the magnetization jump on the basis of the Maxwell
construction. The magnetization jump in the Ising-limit is investigated by
means of perturbation theory. Based on our numerical results, we briefly
discuss the phase diagram of the extended Bose-Hubbard model in the hard-core
limit.
