Interplay of anisotropy and frustration: Triple transitions in a triangular-lattice antiferromagnet

The classical Heisenberg antiferromagnet on a triangular lattice with the single-ion anisotropy of the easy-axis type is studied theoretically. The phase diagram in an external magnetic field is constructed from the mean-field analysis. Three successive Berezinskii-Kosterlitz-Thouless transitions are found by Monte Carlo simulations in zero field. Two upper transitions are related to the breaking of the discrete Z₆ symmetry while the lowest transition is associated with a quasilong-range ordering of transverse components. The intermediate collinear phase between the first and second transition is the critical phase predicted by Jos\'e et al. [Phys. Rev. B 16, 1217 (1977)].