  The classical and the quantum, spin $S=1/2, versions of the uniaxially
anisotropic Heisenberg antiferromagnet on a square lattice in a field parallel
to the easy axis are studied using Monte Carlo techniques. For the classical
version, attention is drawn to biconical structures and fluctuations at low
temperatures in the transition region between the antiferromagnetic and
spin-flop phases. For the quantum version, the previously proposed scenario of
a first-order transition between the antiferromagnetic and spin-flop phases
with a critical endpoint and a tricritical point is scrutinized.
