Icosahedral Skyrmions

Richard A. Battye, Conor J. Houghton, Paul M. Sutcliffe

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this article we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize the energy of Coulomb charges on a sphere, we are led to conjecture a sequence of magic baryon numbers, B = 7,17,37,67,97,..., at which the minimal energy Skyrmion has icosahedral symmetry and unusually low energy. We present evidence for this conjecture by applying a simulated annealing algorithm to compute energy minimizing rational maps for all degrees up to 40. Further evidence is provided by the explicit construction of icosahedrally symmetric rational maps of degrees 37, 47, 67 and 97. To calculate these maps we introduce two new methods for computing rational maps with Platonic symmetries. © 2003 American Institute of Physics.
    Original languageEnglish
    Pages (from-to)3543-3554
    Number of pages11
    JournalJournal of Mathematical Physics
    Volume44
    Issue number8
    DOIs
    Publication statusPublished - 1 Aug 2003

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