Geodesic
Collective excitations in the ferro- and antiferromagnetic states of the two-dimensional repulsive Hubbard model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 229-259 
V. N. Popov; P. A. Sevastianov. Collective excitations in the ferro- and antiferromagnetic states of the two-dimensional repulsive Hubbard model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 229-259. http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a12/
@article{ZNSL_1994_209_a12,
     author = {V. N. Popov and P. A. Sevastianov},
     title = {Collective excitations in the ferro- and antiferromagnetic states of the two-dimensional repulsive {Hubbard} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {229--259},
     year = {1994},
     volume = {209},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a12/}
}
TY  - JOUR
AU  - V. N. Popov
AU  - P. A. Sevastianov
TI  - Collective excitations in the ferro- and antiferromagnetic states of the two-dimensional repulsive Hubbard model
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1994
SP  - 229
EP  - 259
VL  - 209
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a12/
LA  - ru
ID  - ZNSL_1994_209_a12
ER  - 
%0 Journal Article
%A V. N. Popov
%A P. A. Sevastianov
%T Collective excitations in the ferro- and antiferromagnetic states of the two-dimensional repulsive Hubbard model
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 229-259
%V 209
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a12/
%G ru
%F ZNSL_1994_209_a12

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Collective excitations in antiferromagnetic and ferromagnetic states of the two-dimensional repulsive Hubbard model are investigated both in the phase transition vicinity (Ginsburg–Landau region $|T-T_c|\ll T_c$) and in the low-temperature region $T\ll T_c$ using the functional integration region. The collective excitation spectrum consists of one branch at $T>T_c$ and one more branch (Goldstone branch) arises at $T. The Goldstone branch at $T\ll T_c$ in the antiferromagnetic state is calculated including the anisotropic correction term to the linear dispersion law. The value of the non-phonon branch at the zero momentum is equal to the double gap of the fermion energy $2\Delta$. All the spectrum branches in the ferromagnetic state vanish at zero momentum ($\lim_{k\to0}E(k)=0$). Bibliography: 6 titles.