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A phase diagram of the one-dimensional S=1/2 frustrated ferromagnetic Heisenberg model in a magnetic field is studied via a bosonization technique. Besides the ferromagnetic phase, two different nematiclike phases with additional symmetry breaking of reflections about a bond or about a site are mapped out. The prediction is made of possible fourfold degeneracy of a ground state at H=0 for sufficiently strong second-neighbor coupling.
Andrey V. Chubukov (Sun,) studied this question.