  We demonstrate that the Pauli spin-splitting effects in a magnetic field
improve nesting properties of a realistic quasi-one-dimensional electron
spectrum. As a result, a high resistance Peierls charge-density-wave (CDW)
phase is stabilized in high enough magnetic fields in (Per)$_2$Pt(mnt)$_2$
conductor. We show that, in low and very high magnetic fields, the Pauli
spin-splitting effects lead to a stabilization of a soliton wall superlattice
(SWS) CDW phase, which is characterized by periodically arranged soliton and
anti-soliton walls. We suggest experimental studies of the predicted first
order phase transitions between the Peierls and SWS phases to discover a unique
SWS phase. It is important that, in the absence of a magnetic field and in a
limit of very high magnetic fields, the suggested model is equivalent to the
exactly solvable model of Brazovskii, Dzyaloshinskii, and Kirova.
