Heisenberg model on a space with negative curvature: topological spin   textures on the pseudosphere
  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. 
L.R.A. Belo, N.M. Oliveira-Neto, W.A. Moura-Melo, A.R. Pereira, and E.   Ercolessi