2010/10/31 by Juha Jäykkä, Martin Speight
Mathematics · Physics and Astronomy · #Charge (physics) #Cold Atom Physics and Bose-Einstein Condensates #Dipole #Geometry #Magnetic properties of thin films #Massless particle #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Scalar (mathematics) #Scalar field #Skyrmion #Symmetry (geometry) #cond-mat.other #hep-th
paper · pdf · doi:10.1103/physrevd.82.125030
published as Phys.Rev.D82:125030,2010 · v3: replaced with journal version, one new reference, one deleted reference; 8 pages, 5 figures v2: fixed some typos and clarified the relationship with condensed matter systems 8 pages, 5 figures
openalex publication_date 2010/12/22 · arxiv created 2011/02/02 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The baby Skyrme model is studied with a novel choice of potential, V=(1)/(2)\ensuremathφ32. This ``easy plane'' potential vanishes at the equator of the target two-sphere. Hence, in contrast to previously studied cases, the boundary value of the field breaks the residual SO(2) internal symmetry of the model. Consequently, even the unit charge Skyrmion has only discrete symmetry and consists of a bound state of two half lumps. A model of long-range inter-Skyrmion forces is developed wherein a unit Skyrmion is pictured as a single scalar dipole inducing a massless scalar field tangential to the vacuum manifold. This model has the interesting feature that the two-Skyrmion interaction energy depends only on the average orientation of the dipoles relative to the line joining them. Its qualitative predictions are confirmed by numerical simulations. Global energy minimizers of charges B=1,…,14,18,32 are found numerically. Up to charge B=6, the minimizers have 2B half lumps positioned at the vertices of a regular 2B-gon. For charges B\ensuremath≥7, rectangular or distorted rectangular arrays of 2B half lumps are preferred, as close to square as possible.