  We perform exact numeric calculations for the two-orbital Hubbard model on
the four-site cluster. In the limit of large on-site coupling the model becomes
equivalent to the spin $S=1$ Heisenberg model. By comparing energy spectra of
these two models, we quantified the range of interaction parameters for which
the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model.
Then we examined how the spectrum evolves when we are outside of this region,
focusing especially on checking of how it is modified when various ways of
interatomic hoppings of electrons between different orbitals are taken into
account. We finally show how these modifications affect the dependence of
specific heat on temperature.
