Geodesic
Integration of the two-dimensional Heisenberg model by methods of differential geometry
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 302-314

Voir la notice de l'article provenant de la source Math-Net.Ru

The methods of classical differential geometry are used to integrate the two-dimensional Heisenberg model. After the hodograph transformation, the model equations are written in terms of the metric tensor associated with a curvilinear coordinate system and its derivatives. It is shown that their general solution describes all previously known exact solutions except a flat vortex. A new type of vortex structure, a “vortex strip”, is predicted and analyzed in two-dimensional ferromagnets. Its typical properties are the finite dimensions of the domain of definition, the finiteness of the total energy, and the absence of a vortex core in the presence of a vortex structure.
Keywords: Heisenberg model, differential geometry, metric tensor, general solution, vortices, isotropic magnet, vortex street
Mots-clés : exact solutions. 
@article{TMF_2023_216_2_a7,
     author = {A. B. Borisov},
     title = {Integration of the two-dimensional {Heisenberg} model by methods of differential geometry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {302--314},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a7/}
}
TY  - JOUR
AU  - A. B. Borisov
TI  - Integration of the two-dimensional Heisenberg model by methods of differential geometry
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 302
EP  - 314
VL  - 216
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a7/
LA  - ru
ID  - TMF_2023_216_2_a7
ER  - 
%0 Journal Article
%A A. B. Borisov
%T Integration of the two-dimensional Heisenberg model by methods of differential geometry
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 302-314
%V 216
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a7/
%G ru
%F TMF_2023_216_2_a7
A. B. Borisov. Integration of the two-dimensional Heisenberg model by methods of differential geometry. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 302-314. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a7/