3D van der Waals σmodel and its topological excitations
Abstract
It is shown that the 3D vector van der Waals nonlinear σmodel (NSM) on a sphere S^{2} has two types of topological excitations: reminiscent vortices and instantons of 2D NSM. The first ones, the hedgehogs, are described by the homotopic group π_{2}(S^{2}) = Z 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 π_{3}(S^{2}) = Z, or the Hopf invariant HinZ, and have finite energy. The possibility of a topological phase transition in this model and its applications are briefly discussed.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 September 2001
 DOI:
 10.1209/epl/i200100349x
 arXiv:
 arXiv:hepth/0002041
 Bibcode:
 2001EL.....55..788B
 Keywords:

 11.15.Kc;
 11.27.+d;
 61.30.Jf;
 Classical and semiclassical techniques;
 Extended classical solutions;
 cosmic strings domain walls texture;
 Defects in liquid crystals;
 High Energy Physics  Theory;
 Condensed Matter
 EPrint:
 10 pages, Latex2e