Abstract
Commensurate-commensurate phase transitions are known to occur in the Ising model with competing interactions (ANNNI model). We show that an analogous scenario may occur in spin Hamiltonians with continuous symmetry and competing interactions when an external magnetic field is applied. In particular we study a planar square lattice with exchange competition up to third neighbours. We consider exchange competition suitable for giving a zero-temperature-zero-field configuration characterized by a spin-spin turn angle Q=4 pi /5. In contrast with previous conclusions, based on the hypothesis that the unit magnetic cell does not change under the effect of an external magnetic field, we find discontinuous phase transitions between a distorted-helix phase (with five spins per cell) and the spin-flop phase (with two spins per cell) and between the spin-flop phase and a fan phase (with five spins per cell). This behaviour seems to be a general rule for large enough Q as confirmed by the helix with a turn angle Q=6 pi /7 in zero field.
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