Two-dimensional skyrmions on the sphere

We study a model for two-dimensional skyrmions on a sphere of radius L. Suc h model simulates a skyrmion lattice of density W/(2 pi L-2), where W is th e skyrmion winding number. We show that, to a very good approximation, phys ical results depend only on the product alpha L-4, where alpha is the stren gth of potential term. In the range alpha L-4 less than or similar to 3 the order parameter vanishes, there is a uniform distribution of the density o ver the whole surface and the energy of the W = 2 sector lies above twice t he energy of the W = 1 sector. If alpha L-4 greater than or similar to 6 th e order parameter approaches unity and the density concentrates near one of the poles. Moreover the disoliton is always bound. We also present a varia tional solution to the field equations for which the pure alpha L-4-depende nce is exact. Finally, some consequences of our results for the Quantum Hal l Effect are discussed.