Abstract
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.
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