  A self-consistent stochastic model of domain structure formation in a
uniaxial ferroelectric, quenched from a high-temperature paraelectric phase to
a low-temperature ferroelectric phase, is developed with an account of the
applied electric field and the feedback effect via local depolarization fields.
Both polarization and field components are considered as Gauss random
variables. A system of integro-differential equations for correlation functions
of all involved variables is derived and solved analytically and numerically.
Phase diagram in terms of the average value and dispersion of polarization
reveals different possible equilibrium states and available final single-domain
and multi-domain states. The time-dependent evolution of the average
polarization and dispersion discloses a bifurcation behavior and the
temperature-dependent value of the electric field, deciding between the
single-domain and multi-domain final states, which can be interpreted as the
coercive field. Analytical and numerical results for the time-dependent
correlation length and correlation functions exhibit plausible agreement with
available experimental data.
