Classical and quantum two-dimensional anisotropic Heisenberg antiferromagnets

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.