Modified self-consistent harmonic approximation and its application to two-dimensional easy-axis quantum ferromagnets

In the paper we describe the modification of self-consistent harmonic approximation for quantum S=1 systems. This method has a number of advantages in comparison with usual SCHA. We apply the method to two-dimensional ferromagnets with easy-axis exchange or single-site anisotropy. The results are in good agreement with Monte-Carlo simulations and pure-quantum SCHA.