Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight-binding electronic spectra on graphs with spherical topology. I.
  The effect of a magnetic charge   This is the first of two papers devoted to tight-binding electronic spectra
on graphs with the topology of the sphere. In this work the one-electron
spectrum is investigated as a function of the radial magnetic field produced by
a magnetic charge sitting at the center of the sphere. The latter is an integer
multiple of the quantized magnetic charge of the Dirac monopole, that integer
defining the gauge sector. An analysis of the spectrum is carried out for the
five Platonic solids (tetrahedron, cube, octahedron, dodecahedron and
icosahedron), the C$_{60}$ fullerene, and two families of polyhedra, the
diamonds and the prisms. Except for the fullerene, all the spectra are obtained
in closed form. They exhibit a rich pattern of degeneracies. The total energy
at half filling is also evaluated in all the examples as a function of the
magnetic charge.

23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin