Some current problems in perovskite nano-ferroelectrics and multiferroics: kinetically-limited systems of finite lateral size

We describe some unsolved problems of current interest; these involve quantum critical points in<br/>ferroelectrics and problems which are not amenable to the usual density functional theory, nor to<br/>classical Landau free energy approaches (they are kinetically limited), nor even to the Landau–<br/>Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter)<br/>because they are dominated by finite aperiodic boundary conditions.<br/>