Kosterlitz-Thouless and magnetic transition temperatures in layered magnets with a weak easy-plane anisotropy

The two-dimensional (2D) Heisenberg magnet with a weak easy-plane anisotropy is considered. A renormalization-group analysis in this model is performed for both quantum and classical cases. A crossover from the Heisenberg to 2D XY model is discussed. The magnetic transition owing to the interlayer coupling is considered. Analytical results for the Kosterlitz-Thouless and Curie (Neel) temperatures are derived by taking into account two-loop corrections. The results are compared with experimental data, e.g., on K2CuF4, and turn out to provide a quantitative description, unlike the standard one-loop results. [S0163-1829(99)08725-1].