3D van der Waals $σ$-model and its Topological Excitations

Details 3D van der Waals $σ$-model and its Topological Excitations 3D van der Waals $σ$-model and its Topological Excitations

2000-02-05

arxiv.org/abs/hep-th/0002041v1

Europhys.Lett.55:788-794,2001

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex-2e

Scientific paper

10.1209/epl/i2001-00349-x

It is shown that 3D vector van der Waals (conformal) nonlinear $\sigma$-model (NSM) on a sphere $S^2$ has two types of topological excitations reminiscent vortices and instantons of 2D NSM. The first, the hedgehogs, are described by homotopic group $\pi_2(S^2) = \mathbb {Z}$ and have the logarithmic energies. They are an analog of 2D vortices. The energy and interaction of these excitations are found. The second, corresponding to 2D instantons, are described by hpmotopic group $\pi_3(S^2) = \mathbb {Z}$ or the Hopf invariant $H \in \mathbb {Z}$. A possibility of the topological phase transition in this model and its applications are briefly discussed.

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