Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Translation-invariant Gibbs measures for the Blum-Kapel model on a
  Cayley tree
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
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
18
The categories of this paper are: econ
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas