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Abstract
The ground state phase diagram is determined for the frustrated classical Heisenberg
chain with added nearest-neighbor biquadratic exchange interactions. There appear
ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition
occurs at the spiral boundary. The model contains an isotropic version of the ANNNI
model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza
method is not obviously useful due to the non-linear weak-constraint problem; however
the ground state is obtained analytically by the exact cluster method of Lyons and
Kaplan. The results are compared to the model of Thorpe and Blume, where the Heisenberg
part of the energy is not frustrated.