electron with spin $\alpha=\uparrow,\downarrow$ in the $a$ orbital, and $b_\beta^{\vphantom\dagger}$ annihilates an electron with spin $\beta$ in the $b$ orbital. Excitonically ordered states thus have some partial occupation of the nominally excited $a$ states, as a result of Coulombic repulsion. In general, $\Delta_{\alpha\beta}$ is a proper order parameter (i.e. one which characterizes a spontaneously broken symmetry) if the $a$ and $b$ orbitals have different symmetries. In this paper, we consider a “minimal model” with this property, comprised of one $a$ and one $b$ orbital per unit cell – see Fig. \[fig:orbs\]. This mimics the situation in the hexaborides, for which the conduction and valence states also transform as different representations of the cubic point group[@Monnier]. Because of complications arising from orbital degeneracy, however, the appropriate representations for the hexaborides are three-dimensional rather than scalar. We defer the possible complications arising from these additional degrees of freedom to a future investigation.

![Imaginative illustration of a model for which the tight-binding description employed phenomenologically here directly applies. Red circles and blue+green crosses represent $s$ and $d_{xy}$ orbitals, respectively.[]{data-label="fig:orbs"}](sdorbs2.eps){width="2.0in"}

As for the more familiar Hubbard model (see, e.g. Ref. [@Fradkin]), the problem simplifies somewhat in the strong-coupling limit. Considering first the undoped system 