  We investigate the phase diagram and, in particular, the nature of the the
multicritical point in three-dimensional frustrated $N$-component spin models
with noncollinear order in the presence of an external field, for instance
easy-axis stacked triangular antiferromagnets in the presence of a magnetic
field along the easy axis. For this purpose we study the renormalization-group
flow in a Landau-Ginzburg-Wilson \phi^4 theory with symmetry O(2)x[Z_2 +O(N-1)]
that is expected to describe the multicritical behavior. We compute its MS
\beta functions to five loops. For N\ge 4, their analysis does not support the
hypothesis of an effective enlargement of the symmetry at the multicritical
point, from O(2) x [Z_2+O(N-1)] to O(2)xO(N). For the physically interesting
case N=3, the analysis does not allow us to exclude the corresponding symmetry
enlargement controlled by the O(2)xO(3) fixed point. Moreover, it does not
provide evidence for any other stable fixed point. Thus, on the basis of our
field-theoretical results, the transition at the multicritical point is
expected to be either continuous and controlled by the O(2)xO(3) fixed point or
to be of first order.
