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