Generalized helimagnets between two and four dimensions

We study the phase transitions of N-component generalized helimagnets. In the neighborhood of two dimensions, a D = 2 + epsilon renormalization group study reveals a rich fixed point structure as well as a nematiclike phase with partial spin ordering. In the physical case N = 3, relevant to real magnets with noncollinear ordering, we show that this implies an XY-like transition between the ordered phase and the nematiclike phase. A non-Abelian mean-field calculation is shown to lead to the same picture but then the principal chiral fixed point, which had been proposed earlier as the relevant fixed point for D = 3 helimagnets, plays no role due to the appearance of a first-order line.