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The two-dimensional (2D) Heisenberg magnet with a weak easy-plane anisotropyis considered. A renormalization group (RG) analysis in this model is performedfor both quantum and classical cases. A crossover from the Heisenberg to 2D XYmodel is discussed. The magnetic transition owing to the interlayer coupling isconsidered. Analytical results for the Kosterlitz-Thouless and Curie (Neel)temperatures are derived with account of two-loop corrections. The results arecompared with experimental data, e.g. on K2CuF4, and turn out to provide aquantitative description, unlike the standard one-loop results.Comment: 4 pages, RevTeX, 1 figur

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