Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Free energy density for mean field perturbation of states of a
  one-dimensional spin chain
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th