A Chern-Simons-gauged nonlinear Schro{}dinger equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed within the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern-Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex-antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed.
No takes yet. Share an insight, caveat, or question.
Martina et al. (1993) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: