Baby skyrmions on the sphere

We study a model for two-dimensional skyrmions on a sphere of radius L. Such model simulates a skyrmion lattice of density W/(2 πL^2), where W is the skyrmion winding number. We show that, to a very good approximation, physical results depend only on the product αL^4, where αis the strength of potential term. In the range αL^4 approx. or less than 3 the order parameter vanishes, there is a uniform distribution of the density over the whole surface and the energy of the W=2 sector lies above twice the energy of the W=1 sector. If αL^4 approx. or greater than 6 the order parameter approaches unity and the density concentrates near one of the poles. Moreover the disoliton is always bound. We also present a variational solution to the field equations for which the pure αL^4-dependence is exact. Finally, some consequences of our results for the Quantum Hall Effect are discussed.

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