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The phase diagram of the quasi-two-dimensional easy-plane antiferromagneticmodel, with a magnetic field applied in the easy plane, is studied using theself-consistent harmonic approximation. We found a linear dependence of thetransition temperature as a function of the field for large values of thefield. Our results are in agreement with experimental data for the spin-1honeycomb compound BaNi_2V_2O_3

Phase diagram of the antiferromagnetic XY model in two dimensions in a magnetic field