Thermodynamics of two-dimensional XXZ easy-plane quantum Heisenberg magnets

We consider the quantum easy-plane (XXZ) magnet on the square lattice. In the classical case the system exhibits the Berezinskii-Kosterlitz-Thouless transition. Simulations, both for ferro- and antiferromagnets, using the method of the effective classical Hamiltonian, are made for different spin values and refer to the specific heat, the static spin correlation functions and correlation lengths in a broad range of temperatures, below and above the transition. The effects of quantum fluctuations are quantitatively evaluated and discussed.