On the statistical correlations of random polarization and electric depolarization fields in ferroelectrics

A conceptual problem of the electric-field mediated polarization correlations during a stochastic formation of polarization domain structure in ferroelectrics is addressed by using an exactly solvable stochastic model of polarization development in a uniaxial ferroelectric [Phys. Rev. B 107, 144109 (2023)]. A full set of time-dependent two-point correlation coefficients between all random variables is derived analytically, evaluated numerically and presented graphically in 3D. They are particularly required for the analysis of nonlinear phenomena involving spatial dispersion like optical second harmonic generation and scattering.