  To understand the role that degeneracy, hybridization, and nesting play in
the magnetic and pairing properties of multiorbital Hubbard models we here
study numerically two types of two- orbital models, both with hole-like and
electron-like Fermi surfaces (FS's) that are related by nesting vectors ({\pi},
0) and (0, {\pi}). In one case the bands that determine the FS's arise from
strongly hybridized degenerate dxz and dyz orbitals, while in the other the two
bands are determined by non-degenerate and non-hybridized s-like orbitals.
Using a variety of techniques, in the weak coupling regime it is shown that
only the model with hybridized bands develops metallic magnetic order, while
the other model exhibits an ordered excitonic orbital-transverse spin state
that is insulating and does not have a local magnetization. However, both
models display similar insulating magnetic stripe ordering in the strong
coupling limit. These results indicate that nesting is a necessary but not
sufficient condition for the development of ordered states with finite local
magnetization in multiorbital Hubbard systems; the additional ingredient
appears to be that the nested portions of the bands need to have the same
orbital flavor. This condition can be achieved via strong hybridization of the
orbitals in weak coupling or via the FS reconstruction induced by the Coulomb
interactions in the strong coupling regime. This effect also impacts the
pairing symmetry as demonstrated by the study of the dominant pairing channels
for the two models.
