Integration of the two-dimensional Heisenberg model by methods of differential geometry

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 gen...

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Bibliographic Details
Published inTheoretical and mathematical physics Vol. 216; no. 2; pp. 1168 - 1179
Main Author Borisov, A. B.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Differential geometry
Exact solutions
Ferromagnetism
Heisenberg theory
Hodographs
Mathematical and Computational Physics
Physics
Physics and Astronomy
Spherical coordinates
Statistical models
Tensors
Theoretical
Two dimensional analysis
Two dimensional models
Vortices
vortex street
exact solutions
isotropic magnet
Heisenberg model
differential geometry
general solution
vortices
metric tensor
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Summary: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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577923080081