Geodesic
The effective action and the collective modes spectrum in the antiferromagnetic phase of the three--band repulsive Hubbard model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 216-230

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The paper is concerned with the application of path integration (successive integration over “fast” and “slow” variables and the Hubbard–Stratonovich transformation) to the antiferromagnetic state in the three-band two dimensional repulsive Hubbard model. It is shown that the model under consideration is equivalent in the lowest approximation to the half–filled single–band Hubbard model. The effective action for the collective Bose-fields, the critical temperature of the phase transition and the exitations spectra are obtained. 
@article{ZNSL_1997_245_a11,
     author = {V. S. Kapitonov and K. L. Malyshev and V. N. Popov and P. A. Sevastianov},
     title = {The effective action and the collective modes spectrum in the antiferromagnetic phase of the three--band repulsive {Hubbard} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {216--230},
     publisher = {mathdoc},
     volume = {245},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a11/}
}
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V. S. Kapitonov; K. L. Malyshev; V. N. Popov; P. A. Sevastianov. The effective action and the collective modes spectrum in the antiferromagnetic phase of the three--band repulsive Hubbard model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 216-230. http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a11/