Self-consistent mean-field study of the anisotropic two-dimensional XY model

The self-consistent harmonic approximation is applied to the classical two-dimensional anisotropic XY (planar rotator) model on the square lattice. From the effective spin-wave stiffness constant data the phase diagram is constructed and the corresponding lattice dimensionally crossover exponents are defined and found. The variation of the stiffness constant jump with the anisotropy magnitude is obtained and the scaling functions ε(X) are extracted.