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Correlation Effects in Itinerant Magnetism

In this contribution we would like to revisit the problems of ferromagnetism (F) and antiferromagnetism (AF) in the pure itinerant model. These methods can be extended later to the superconducting materials. In our model we assume the extended Hubbard Hamiltonian. Transition from the paramagnetic state to the ordered state of magnetic nature is decided by the competition between kinetic and potential energy in which there is an increase in the kinetic energy moderated by the inter-site interactions, and a decrease in the potential energy. The competition between these two energies results in the existence of critical values of interactions for creating magnetic alignment. Only when existing in a given material interaction exceeds the critical value for a given type of ordering we can have the alignment of this type. The influence of inter-site correlation on F and AF in the presence of Coulomb on-site correlation is investigated. The well known Landau free energy expansion is corrected for both F and AF ordering to reflect the presence of critical interaction in the second order term, which leads to the magnetic alignment. The numerical results show that the inter-site interactions favor F at the end of the band and AF at the half-filled point. In both cases of F and AF ordering, these interactions lower substantially the Curie and Neel's temperature towards experimental data. This helps to remove the paradox in magnetism that has persisted for a long time.