Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-size Analysis of $O(N)$ Nonlinear $\sigma$ Model on Semi-compact
  Spaces   Fisher's phenomenological renormalization method is used to calculate the
mass gap and the correlation length of the $O(N)$ nonlinear $\sigma$ model on a
semi-compact space $S^{1}\times {\bf R}^{2}$. This shows that the ultraviolet
momentum cut-off does not conflict with the infrared cut-off along the $S^{1}$
direction. The mass gap on $S^{2}\times {\bf R}$ is also discussed.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci