Topological spin excitations on a rigid torus

We study the Heisenberg model of classical spins lying on a 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 ->infinity, 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. Vortexlike configurations are also supported: in a ring torus (R > r), such excitations present no core where energy could blow up. At the limit R ->infinity, we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, which yields 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 it vanishesm we recover a vortex configuration on a sphere.