QUANTUM FLUCTUATIONS IN THE AXIAL NEXT-NEAREST-NEIGHBOR ISING-MODEL

We obtain the axial next-nearest-neighbor Ising model from a Heisenberg model with large single-ion anisotropy energy, D, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in 1/S at zero temperature within an expansion in J/D, where J is an exchange energy. The transition from the state with periodicity p = 4 to the uniform state ( p = ∞) occurs via a sequence of first order transitions in which p increases monotonically.