Frustrated classical Heisenberg model in one dimension with nearest-neighbor biquadratic exchange: Exact solution for the ground-state phase diagram

The ground-state phase diagram is determined exactly for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) phases, and disordered states. The model contains an isotropic version of the antiferromagnetic next-nearest-neighbor Ising model, i.e., an isotropic Ising model. It is closely related to a model proposed for some manganites, suggesting a possible mechanism for the observed uudd state.