Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Product type potential on the $X\,Y$ model: selection of maximizing
  probability and a large deviation principle
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess