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Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere

L. R. A. Belo·N. M. Oliveira-Neto·W. A. Moura-Melo·A. R. Pereira·E. Ercolessi
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Abstract

Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at least a hole is incorporated. We also address the issue of `in-plane' vortices, in the XY regime. Interestingly, the energy of a single vortex no longer blows up as the excitation spreads to infinity. This yields a non-confining potential between a vortex and a antivortex at large distances so that the pair may dissociate at arbitrarily low temperature.

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L. R. A. Belo, N. M. Oliveira-Neto, W. A. Moura-Melo, A. R. Pereira, E. Ercolessi. 2006-12-22. Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere. https://doi.org/10.1016/j.physleta.2007.01.044

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