Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect observables for the hierarchical non-linear $O(N)$-invariant
  $\sigma$-model   We compute moving eigenvalues and the eigenvectors of the linear
renormalization group transformation for observables along the renormalized
trajectory of the hierarchical non-linear $O(N)$-invariant $\sigma$-model by
means of perturbation theory in the running coupling constant. Moving
eigenvectors are defined as solutions to a Callan-Symanzik type equation.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc