Hopf Solitons on the Lattice
Abstract
Hopf solitons in the Skyrme-Faddeev model -- S2-valued fields on R3 with Skyrme dynamics -- are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S2-valued fields on the cubic lattice Z3 with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably similar to that of their continuum counterparts, and they exhibit the same power-law relation E ≈ c H3/4 between the energy E and the Hopf number H.
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