Excitonically ordered states are characterized by an off-diagonal order parameter describing pairing between conduction electrons and valence holes. Early theoretical work by Volkov [*et. al.*]{}[@Volkov] anticipated the emergence of ferromagnetism on doping such an excitonic state. These authors considered the limit of nearly nested overlapping conduction and valence bands with [*weak*]{} repulsive electron-electron interactions. In this limit, the problem can be approximately cast into a form nearly identical to BCS theory, and studied using the techniques of mean-field theory. Although this work (and some subsequent recent studies[@Anisimov]) suffers from the important physical mistake of neglecting the instability to phase separation, ferromagnetism remains nevertheless a generic feature in a corrected treatment.[@BalentsVarma; @Barzykin] 

While the appearance of ferromagnetism in the weak-coupling limit is encouraging, it is far from a conclusive and complete theoretical explanation for the experiments. First, Coulomb interactions in the hexaborides are not particularly weak, and most likely are comparable to the Fermi energy and band overlap. Second, the above explanation appears to hinge on the first-order nature of the excitonic to normal (E-N) transition in the BCS limit. While this feature, mathematically analogous to the first-order transition to the normal state due to pair-breaking by an external Zeeman field 