Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group theoretical analysis of structural instability, vacancy ordering
  and magnetic transitions in the system troilite (FeS) - pyrrhotite
  (Fe$_{1-x}$S)
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
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg