Figure 1:
Profiles of 
vs. distance r from the vortex center,
for single static out-of-plane vortices at the center of a circular system
with 180 sites on a square lattice. The curves are labelled by the different
values of 
.
These results were obtained by the relaxation procedure described in the text
(Sec. ii), using a fixed boundary condition as described in
Sec. iv.
Now the approach is to make the spinwave perturbation calculation using the
directions, 
, as the different local quantization axes for
each site. This is similar in spirit to a spinwave calculation for an
antiferromagnet, [25] in which the classical ground state can have
sets of spins on the different sublattices aligned along different directions,
and the perturbation analysis uses different coordinate systems for different
sublattices.