Over a spatial continuum, it is easy to see why some topologicalsolitons like vortices and monopoles have to be stable. For similarreasons, Skyrmions also have to be stable, with a conservedtopological density. The reason is nontrivial homotopy.
Surprisingly, in some phases, but not all phases, the analog oftopological solitons, or at least what can be interpreted as them,also emerge over lattice models. Why is that? There is nonontrivial homotopy over a lattice. Why are there some phases ofthe XY-model with deconfined vortices and antivortices? Why aredeconfined monopoles present in some 3D lattice models?
