  We work out the magnetization and susceptibility of Heisenberg- and
  XXZ-model antiferromagnet spin-1/2 systems in $D$ dimensions under a rigorous
constraint of single particle site occupancy. Quantum fluctuations are taken
into account up to the first order in a loop expansion beyond the N\'eel state
mean field solution. We discuss the results, their validity in the vicinity of
the critical point and compare them with the results obtained by means of a
spin wave approach.
