  We investigate the total energies of spontaneous spin-valley polarized states
in bi-, tri-, and tetralayer rhombohedral graphene where the long-range Coulomb
correlations are accounted for within the random phase approximation. Our
analysis of the phase diagrams for varying carrier doping and perpendicular
electric fields shows that the exchange interaction between chiral electrons is
the main driver of spin-valley polarization, while the presence of Coulomb
correlations brings the flavor polarization phase boundaries to carrier
densities close to the complete filling of the Mexican hat shape top at the
Dirac points. We find that the tendency towards spontaneous spin-valley
polarization is enhanced with the chirality of the bands and therefore with
increasing number of layers.
