  The hierarchical reference theory (HRT) is generalized to spins of
dimensionality $D$. Then its properties are investigated by both analytical and
numerical evaluations for supercritical temperatures. The HRT is closely
related to the self-consistent Ornstein-Zernike approximation (SCOZA) that was
developed earlier for arbitrary $D$. Like the $D=1$ case we studied earlier,
our investigation is facilitated by a situation where both HRT and SCOZA give
identical results with a mean spherical model (MSM) behavior (i.e. $D=\infty$).
However, for the more general situation we find that an additional intermediate
term appears. With an interplay between leading and subleading contributions,
simple rational numbers, independent of $D$ ($<\infty$), are found for the
critical indices.
