Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: An extremality of the translation-invariant Gibbs measure for the
  HC-model on a Cayley tree
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci