  The impact of long-range spin-spin correlations on the structure of a flat
portion in single-particle spectra $\xi(p)$, which emerges beyond the point,
where the Landau state loses its stability, is studied. We supplement the
well-known Nozieres model of a Fermi system with limited scalar long-range
forces by a similar long-range spin-dependent term and calculate the spectra
versus its strength $g$. It is found that Nozieres results hold as long as
$g>0$. However, with $g$ changing its sign, the spontaneous magnetization is
shown to arise at any nonzero $g$. The increase of the strength $|g|$ is
demonstrated to result in shrinkage of the domain in momentum space, occupied
by the flat portion of $\xi(p)$, and, eventually, in its vanishing.
