Two-dimensional ferroelectric liquid crystals

Abstract

The possibility of experimentally realizing two-dimensional $\mathrm{XY}$ critical behavior in thin ferroelectric smectic films is explored. We show that a nonferroelectric smectic-$C$ film will exhibit $\mathrm{XY}$ behavior and then consider the effect of dipolar interactions and external electric field. The dipolar forces stabilize the ferromagnetic order and are relevant along the entire $\mathrm{XY}$ fixed line. They may, however, have little effect on the critical behavior of the present experimental systems due to their small dipole moment. We also offer some comments on the critical behavior controlled by the infinite dipolar fixed point.