Size and Time Rescaling at the Paraelectric to Ferroelectric Phase Transition in BaTiO₃

We describe length and time rescaling across the paraelectric to ferroelectric phase transition in BaTiO$_3$. Small ferroelectric clusters are unable to grow in the paraelectric phase and exist for a short period of time only. The onset of the phase transition invokes a rescaling of both size and time lenghts as necessary ingredients for ferroelectricity to come into existence. The growing of ferroelectric domains involves correlated chains of Ti-O dipoles, which causes domain wall rigidity and domain shape stability. Ferroelectric nanodomains may host islands of opposite polarization (antiferroelectric defects), which appear as an intrinsic feature of the growing BaTiO$_3$ ferroelectric material