Banana- and pizza-slice-shaped mesogens give a new constrained O(n) ferromagnet universality class

It has been known that at high density, banana-shaped molecules are packed into a bent configuration locally, giving rise to interesting liquid-crystalline phases such as splay bend and twist bend. These spontaneous bend states can be modeled theoretically by allowing the bend elastic constant in the Frank elastic energy to become negative. Here, we extend this idea to banana-shaped and pizza-slice-shaped molecules with ferrointeractions, which can display both splayed and bent states. We model this by allowing both splay and bend elastic constants in the effective Frank elastic energy to be negative. In particular, we predict two new liquid-crystalline splay-bend phases. Furthermore, using renormalization group analysis, we showed that the phase transition belongs to a new constrained ferromagnet universality class.