  Various auxiliary-particle approaches to treat electron correlations in
many-electron models are analyzed. Applications to copper-oxide layered systems
are discussed. The ground-state magnetic phase diagrams are considered within
the Hubbard and $s$-$d$ exchange (Kondo) models for square and simple cubic
lattices vs. band filling and interaction parameter. A generalized Hartree-Fock
approximation is employed to treat commensurate ferro-, antiferromagnetic, and
incommensurate (spiral) magnetic phases, and also magnetic phase separation.
The correlations are taken into account within the Hubbard model by using the
slave-boson approach. The main advantage of this approach is correct estimating
the contribution of doubly occupied states number and therefore the
paramagnetic phase energy.
