This article is cited in 4 papers

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

A. B. Borisov

Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: 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, exact solutions.

PACS: 02.30.Ik

MSC: 34A05, 82D40

Received: 14.02.2023
Revised: 13.03.2023

DOI: 10.4213/tmf10481

 English version: Theoretical and Mathematical Physics, 2023, 216:2, 1168–1179

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