Generalized Helimagnets between Two and Four Dimensions

Abstract

We study the phase transitions of N-component generalized helimagnets. In the neighborhood of two dimensions, a $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2+\ensuremath{\epsilon}$ renormalization group study reveals a rich fixed point structure as well as a nematiclike phase with partial spin ordering. In the physical case $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, 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 $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ helimagnets, plays no role due to the appearance of a first-order line.