On topological spin excitations on a rigid torus

Abstract

We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, $R\to \infty$, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R=0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus ($R>r$) such excitations present no core where energy could blow up. At the limit $R\to \infty$ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus ($R=r$) a singular core takes place, while for $R<r$ (spindle torus) two such singularities appear. If $R$ is further diminished until vanish we recover vortex configuration on a sphere.

11 pages, 9 figures

References in corpus (7)

• Bose-Einstein condensation in a circular waveguide
• Topological susceptibility at zero and finite $T$ in SU(3) Yang-Mills theory
• Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere
• Analytical and Monte Carlo study of two antidots in magnetic nanodisks with vortex-like magnetization
• Magnetic vortex-like excitations on a sphere
• Heisenberg Spins on an Elastic Torus Section
• Novel scaling behavior of the Ising model on curved surfaces

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