Over a spatial continuum, it is easy to see why some topological solitons like vortices and...

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Physics

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?

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4.3 Ratings (953 Votes)

I was wondering about exactly the same question some days ago reading the seminal paper of Mermin Rev Mod Phys 51 591648 1979 The topological theory of defects in ordered media where you find an introductory discussion for the example of spins within the twodimensional plane There you find a lot of plots with spins depicted as arrows in the plane See Answer

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