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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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