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∞, 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∞ 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.