The ferromagnetic planar model in the presence of uniaxial single-site anisotropy

Considering spin operators in terms of boson operators, we employ the coherent state path integral approach to study the Heisenberg planar XY model in the presence of uniaxial anisotropy of the form -D(S-i(x))(2) with the x direction parallel to the easy axis. The critical temperatures T-c below which a ferromagnetic phase appears, are obtained as a function of the anisotropy D, and the effects of the anisotropy on the phase transition of the model are examined. We find that in the limits D = 0 and infinity, our results give finite values of the critical temperatures T-c, contrary to those obtained in the molecular field approximation. We show the consistency between our results and those obtained by Lovesey and BaIcar.