The actual mechanism of polarization switching in ferroelectrics remains a
puzzle for many decades, since the usually estimated barrier for nucleation
and growth is insurmountable ("paradox of the coercive field"). To analyze
the mechanisms of the nucleation we consider the exactly solvable case of
a ferroelectric film with a "dead" layer at the interface with electrodes.
The classical nucleation is easier in this case but still impossible, since
the calculated barrier is huge. We have found that the interaction between
the nuclei is, however, long range, hence one has to study an ensemble of
the nuclei. We show that there are ensembles of small (embryonic) nuclei th
at grow without the barrier. We submit that the interaction between nuclei
is the key point for solving the paradox.