The ripple phase in phosphatidylcholine (PC) bilayers has never been explained. Our group has developed some simple (XYZ) spin-lattice models that allow spins to vary their elevation as well as their orientation. The extra degree of freedom allows hexagonal lattices of spins to find states that break out of the normally frustrated randomized states and are stabilized by long-range anti-ferroelectric ordering. To break out of the frustrated states, the spins must form "rippled" phases that make the lattices effectively non-hexagonal.

Image (and research) courtesy Xiuquan Sun