Geodesic
Elementary excitations in the~Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 415-419

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The diagram technique for atomic operators in the ladder approximation is used to obtain results in the theory of Fermi-liquids and these are expressed in terms of the parameters of the Hubbard model. The phase transitions which arise in the system when the number of electrons changes are considered. Comparison of the ground-state energies of the paramagnetic and ferromagnetic phases makes it possible to estimate the corresponding concentrations. 
@article{TMF_1982_50_3_a11,
     author = {A. V. Vedyaev and V. A. Ivanov},
     title = {Elementary excitations in {the~Hubbard} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {415--419},
     publisher = {mathdoc},
     volume = {50},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a11/}
}
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A. V. Vedyaev; V. A. Ivanov. Elementary excitations in the~Hubbard model. Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 415-419. http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a11/