  Only a few years have passed since discovery of polar nematics, and now they
are becoming the most actively studied liquid crystal materials. Despite
numerous breakthrough findings made recently, a theoretical systematization is
still lacking. In the present paper we are making a step on the way of
systematization. A powerful technique that molecular-statistical physics is has
been applied to an assembly of polar molecules influenced by electric field.
Totally, the three polar nematic phases were found to be stable at various
conditions: the double-splay ferroelectric nematic $N_F^{2D}$ (observed in the
lower-temperature range in the absence or at low electric field), the
double-splay antiferroelectric nematic $N_{AF}$ (observed at intermediate
temperature in the absence or at low electric field) and the single-splay
ferroelectric nematic $N_F^{1D}$ (observed at moderate electric field at any
temperature below transition into paraelectric nematic $N$ and in the
higher-temperature range (also below $N$) at low electric field or without it.
A paradoxal transition from $N_F^{1D}$ to $N$ induced by application of higher
electric field has been found and explained. A transformation of the structure
of polar nematic phases at application of electric field has also been
investigated by Monte Carlo simulations and experimentally by observation of
POM images. In particular, it has been realized that, at planar anchoring,
$N_{AF}$ in the presence of moderate out-of-plane electric field exhibits the
twofold splay modulation: antiferroelectric in the plane of the substrate and
ferroelectric in the plane normal to the substrate. Several additional
sub-transitions related to fitting confined geometry of the cell by the
structure of polar phases were detected.
