An exactly solvable model ternary solution with strong three-body interactions

We consider a three-component model of rodlike molecules AA, BB, and AB, confined to the bonds of the honeycomb or three-coordinated Bethe lattice, and with three-body interactions between the molecular ends near a common lattice site. The model is equivalent to an Ising model on an associated lattice and has been previously transformed first to an Ising model on an intermediate lattice then to a standard Ising model on the original honeycomb or Bethe lattice. The exact coexistence curves for phase separation have been previously calculated for weak three-body interactions. In the present paper the same transformations are used for the case of strong three-body interactions, the difference being that in this case the Ising parameters on the intermediate lattice are complex. Exact, closed-form expressions are obtained for the two-phase coexistence surface in temperature-composition space. The exact coexistence curves are drawn for various values of a reduced three-body coupling constant and the reduced temperature. It is proved there is no phase separation in the model on these lattices if the reduced three-body coupling constant is sufficiently large.