Kapitanov, V. S.; Malyshev, C. L.; Popov, V. N.; Sevastianov, P. A. The effective action and the spectrum of collective modes in the antiferromagnetic phase of the three-band repulsive Hubbard model. (English. Russian original) Zbl 0978.82029 J. Math. Sci., New York 100, No. 2, 2147-2155 (2000); translation from Zap. Nauchn. Semin. POMI 245, 216-230 (1997). Summary: 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, in the lowest approximation, the model under consideration is equivalent 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 spectra of excitations are obtained. MSC: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B26 Phase transitions (general) in equilibrium statistical mechanics Keywords:application of path integration; Hubbard-Stratonovich transformation; antiferromagnetic state; repulsive Hubbard model; effective action; critical temperature; phase transition; spectra of excitations PDF BibTeX XML Cite \textit{V. S. Kapitanov} et al., J. Math. Sci., New York 100, No. 2, 1 (1997; Zbl 0978.82029); translation from Zap. Nauchn. Semin. POMI 245, 216--230 (1997)