The quantum easy-plane ferro- and antiferromagnet

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is peculiar of two-dimensional magnetic systems with easy-plane anisotropy. Their prototype is the classical planar (or XY) model, that neglects the role of the out-of-plane spin component. The latter is accounted for in the (easy-plane) XXZ model, that has been studied on a square two-dimensional lattice. From Monte Carlo simulation for the classical XXZ model the classical transition temperature T_BKT^cl turns out to be considerably lower than that of the planar model. The quantum XXZ model is approached by the pure-quantum self-consistent harmonic approximation, which leads to the investigation of an effective classical model. Quantum fluctuations reduce the effective exchange interaction, resulting in a lower BKT transition temperature T_BKT.