Critical behavior of the 2D easy-plane ferromagnet

The critical behavior of 2D magnetic easy-plane systems has mainly been studied by the classical XY model. However, the z-components of the spins have to be considered in order to describe real systems, and their fluctuations cannot positively be neglected when quantum effects are to be included, quantum spins being intrinsically three-component objects. Therefore, Monte Carlo simulations are performed for the Heisenberg ferromagnet with easy-plane anisotropy (XXZ model) on a two-dimensional square lattice with a twofold aim: firstly, to obtain accurate quantitative results about the critical behavior of the classical model, showing the relevant role played by the out-of-plane fluctuations; secondly, to open the way for approaching the quantum thermodynamics by means of the effective Hamiltonian method, that reduces the quantum thermodynamics of the XXZ ferromagnet to the investigation of an effective classical model with temperature dependent renormalized interaction parameters. Specific heat, magnetic susceptibility and correlation length are calculated in the critical region for lattice sizes up to 128x128. These quantities preserve the Kosterlitz-Thouless behavior of the XY model. For the transition temperature of the classical XX0 model we obtain the estimate kBTc/JS^2=0.69±0.01.