Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-08-27
JHEP 9809:012,1998
Physics
High Energy Physics
High Energy Physics - Theory
9 pages (cover and figs. included), Latex, 2 EPS-figs. included
Scientific paper
10.1088/1126-6708/1998/09/012
We study a model for two-dimensional skyrmions on a sphere of radius L. Such model simulates a skyrmion lattice of density W/(2 \pi L^2), where W is the skyrmion winding number. We show that, to a very good approximation, physical results depend only on the product \alpha L^4, where \alpha is the strength of potential term. In the range \alpha L^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 \alpha L^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 \alpha L^4-dependence is exact. Finally, some consequences of our results for the Quantum Hall Effect are discussed.
Bes Daniel R.
Scoccola Norberto N.
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