van der Waals σ-model and its topological excitations
L. D. Landau Institute - Kosyghin Str. 2, Russia, 117334 and
Max Planck Institute - Nothnitzer Str. 38, Dresden, Germany
Accepted: 27 June 2001
It is shown that the 3D vector van der Waals nonlinear σ-model (NSM) on a sphere S2 has two types of topological excitations: reminiscent vortices and instantons of 2D NSM. The first ones, the hedgehogs, are described by the homotopic group and have logarithmic energies. They are an analog of 2D vortices. The second ones, corresponding to 2D instantons, are the hopfions. They are described by the homotopic group , or the Hopf invariant , and have finite energy. The possibility of a topological phase transition in this model and its applications are briefly discussed.
PACS: 11.15.Kc – Classical and semiclassical techniques / 11.27.+d – Extended classical solutions; cosmic strings, domain walls, texture / 61.30.Jf – Defects in liquid crystals
© EDP Sciences, 2001