Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized boundary condition, free energies of six-vertex models and
  fractal dimension   The structures of the configuration space of the six-vertex models with
various boundaries and boundary conditions are investigated, and it is derived
that the free energies depend on the boundary conditions, and that they are
classified by the fractal structures. The "n-equivalences" of the boundary
conditions are defined with a property that the models with n-equivalent
boundary conditions result in the identical free energy. The configurations
which satisfy the six-vertex restriction are classified, through the
n-equivalences, into sets of configurations called islands. It is derived that
each island shows a fractal structure when it is mapped to the real axis. Each
free energy is expressed by the weighted fractal dimension (multi-fractal
dimension) of the island. The fractal dimension of the island has a strict
relation with the maximum eigenvalue of the corresponding block element of the
transfer matrix. It is also found that the fractal dimensions of islands take
the absolute maximum when the boundary is "alternative"; in this case, the free
energy equals to the solution obtained by Lieb and Sutherland.

21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph