Star-triangle equations and multicomponent chiral Potts models

Under certain conditions lipid-bilayer membranes exhibit an incommensurate ripple phase. Pearce and Scott have proposed lattice models with either next-nearest-neighbor interactions or with chiral nearest-neighbor interactions to study this phenomenon. After briefly discussing the equivalence of these two points of view, we present the results of our first search for solutions of the star-triangle equations for multicomponent chiral Potts models, generalizing some of the biomembrane models. In the nonchiral limit, the results apply also to the (Nα,Nβ) model of Domany and Riedel describing the adsorption of molecules on the surface of a crystal.