Phase transitions in anisotropic two-dimensional quantum antiferromagnets

We study the thermodynamic properties of anisotropic two-dimensional quantum antiferromagnets, with both easy-plane and easy-axis anisotropy. We make use of the Quantum Monte Carlo (QMC) method based on the continuous-time loop algorithm. For S = 1/2 and very small anisotropies our QMC data reveal that both the Ising and Berezinskii-Kosterlitz-Thouless universality class (for the easy-axis and easy-plane models, respectively) are well observed and that the critical temperature remains finite even for anisotropies as small as 10(-3), i.e. comparable to the anisotropies measured in real layered compounds; this result rules out the possibility of quantum fluctuations to destroy the finite-temperature transition before the isotropic limit is reached. The phase diagram of the S = 1/2 2d-XXZ antiferromagnet in the region of small anisotropies is then presented.