Detection ofXYBehavior in Weakly Anisotropic Quantum Antiferromagnets on the Square Lattice

We consider the Heisenberg antiferromagnet on the square lattice with $S=1/2$ and very weak easy-plane exchange anisotropy; by means of the quantum Monte Carlo method, based on the continuous-time loop algorithm, we find that the thermodynamics of the model is highly sensitive to the presence of tiny anisotropies and is characterized by a crossover between isotropic and planar behavior. We discuss the mechanism underlying the crossover phenomenon and show that it occurs at a temperature which is characteristic of the model. The expected Berezinskii-Kosterlitz-Thouless transition is observed below the crossover: a finite range of temperatures consequently opens for experimental detection of noncritical 2D $XY$ behavior. Direct comparison is made with uniform susceptibility data relative to the $S=1/2$ layered antiferromagnet ${\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$.