  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.

Strongly Correlated Electrons;Statistical Mechanics