Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin-projection orientations in the plane square-lattice Ising model
  with periodic boundary conditions   The periodic boundary conditions changed the plane square-lattice Ising model
to the torus-lattice system which restricts the spin-projection orientations.
Only two of the three important spin-projection orientations, parallel to the
x-axis or to the y-axis, are suited to the torus-lattice system. The
infinitesimal difference of the free-energies of the systems between the two
systems mentioned above makes their critical temperatures infinitely close to
each other, but their topological fundamental groups are distinct.

20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int