Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competition and coexistence of magnetic and quadrupolar ordering   The large number of low-lying states of d- and f-shells supports a variety of
order parameters. The effective dimensionality of the local Hilbert space
depends on the strength, and kind, of intersite interactions. This gives rise
to complicated phase diagrams, and an enhanced role of frustration and
fluctuation effects. The general principles are illustrated on the example of
the effect of a magnetic field on quadrupolar phase transitions in some
Pr-based skutterudite compounds.

23
The categories of this paper are: solv-int
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an