Low temperature phases of the Andelman-de Gennes model of chiral discrimination: rigorous results

We determine the ordered low temperature phases of the Andelman-de Gennes model of chiral discrimination, using rigorous statistical mechanical methods. The system is considered in the close-packed regime, equivalent to placing the molecules at every site of a honeycomb lattice. If the system contains an equimolar mixture of each of a pair of enantiomers, we prove in general that a heterochiral phase (disfavoring enantiomeric segregation) as well as a homochiral phase (favoring the segregation) is possible, depending on the types of intermolecular interactions. We apply our general results to the specific examples of the interactions considered by Andelman and de Gennes and provide a comparison with their conjectures that were based on two-molecule partition functions.