Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Improved Bounds on the Phase Transition for the Hard-Core Model in
  2-Dimensions
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th