Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A topological phase transition on the edge of the 2d $\mathbb{Z}_2$
  topological order
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci