Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical region of D-dimensional spins: Extension and analysis of the
  hierarchical reference theory   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.

0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph