An exactly solvable model ternary solution with three-body interactions

A ternary solution is considered in which molecules of types AA, BB, and AB occupy the bonds of a honeycomb lattice or a three-coordinate Bethe lattice. The three molecular ends near a common lattice site interact with arbitrary three-body interactions εAAA, εAAB, εABB and εBBB. The model is shown to be equivalent to a spin-12 Ising model on the same lattice with a field but with only pairwise interactions. Asymmetric two-phase coexistence surfaces are calculated exactly for the model on the two lattices. The behavior of the coexistence diameter in the neighborhood of the critical point is studied for the limiting case of the model in which only AA and BB molecules are present.