  Initial conditions after quenching from a high-temperature paraelectric phase
to a low-temperature ferroelectric phase have a substantial impact on the
temporal development and formation of stable polarization domain structures
which eventually determine physical properties and the functionality of
ferroelectrics. Based on the recently advanced exactly solvable model of the
stochastic domain structure kinetics in a uniaxial ferroelectric [Phys. Rev. B
107, 144109 (2023)], we study the effect of the magnitude of the initial
disorder, its initial correlation length and polarization correlation function
on the system evolution. For different shapes of the initial correlation
function, the time-dependent correlation length and the two-point polarization
correlation coefficient are calculated analytically demonstrating universal
features and a good agreement with the available experimental data.
Particularly, the magnitude of the charge density correlation function reveals
a strong reduction of the bound charges at the nominally charged domain walls
which was recently observed experimentally in uniaxial ferroelectrics.
Consequently, the integrodifferential equations of evolution for the
polarization correlation function and the mean polarization are numerically
solved for different initial conditions. The temporal dependence of the
polarization mean value and variance are evaluated demonstrating the
bifurcation behavior depending on the applied electric field. The impact of the
initial state properties on the coercive field deciding between the single- and
multi-domain final states of the system is disclosed.
