Abstract
In this paper we study the quantum phase transition in a three-dimensional XY model with single-ion anisotropy D and spin S = 1 . The low D phase is studied using the self consistent harmonic approximation, and the large D phase using the bond operator formalism. We calculate the critical value of the anisotropy parameter where a transition occurs from the large- D phase to the Néel phase. We present the behavior of the energy gap, in the large- D phase, as a function of the temperature. In the large D region, a longitudinal magnetic field induces a phase transition from the singlet to the antiferromagnetic state, and then from the AFM one to the paramagnetic state.
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