For comparison, Fig. 10 shows the lowest modes on the 180-site system
in the absence of the vortex, at 
, starting instead from a
ferromagnetically aligned state. Some modes, including the one that most
resembles the soft mode when the vortex is present, do not appear very
different whether the vortex is present or absent (for this value of 
far from 
). On the other hand, some modes, such as (b) and (d),
clearly have amplitude at the vortex core that is not present when the vortex
is removed.
Figure 10:
Maps of the spin fluctuations in a square lattice system as in
Fig. 7, but without a vortex present, for 
In
comparing with Fig. 7,
modes (b1), (b2), and (d) there have extra fluctuations present due to the vortex,
at its core, not seen here in the absence of the vortex.