calculation and the stoichiometric behavior, we arrive at the partial phase diagram in Fig. \[partialfig\]. This is in agreement with the general expectations stated above. It should be stressed, however, that this analysis of doping is far from exhaustive. More detailed investigations of both the weak and strong coupling limits are currently underway[@Veillette] The remainder of the paper is structured as follows. In Sec. \[sec:model\], we present a detailed exposition of the (simplest) tight-binding model capable of describing excitonically-ordered states, and consider the limit of infinite interaction strength. The bulk of the paper is contained in Sec. \[sec:undoped\], where the model is analyzed for large but finite interactions, focusing on the stoichiometric situation with two valence electrons per unit cell. For this electron density the model is insulating, but can sustain excitonic and other types of ordering. The properties of the model with doping are discussed in Sec. \[sec:doping\]. We conclude in Sec. \[sec:discussion\] with a clarifying discussion delineating the physical properties of various possible excitonic insulators, and the relation of the results of this paper to the hexaborides.

Tight-Binding Model {#sec:model}
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“On-site” terms
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We consider a minimal model capable of exhibiting excitonic order, which contains two orbitals 