Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Disproportionation Transition at Critical Interaction Strength:
  Na$_{1/2}$CoO$_2$
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th