Calculations on systems with 
were made. For the fixed
boundary condition used, the lowest frequency mode is the mode which becomes
soft at some 
. On the other hand, when free boundary
conditions are used, there are also a few modes that can lie below the soft
mode, reflecting the greater freedom of movement of the boundary spins; the
lowest mode is at 
corresponding to a uniform rotation of all the
spins in the easy-plane, a motion that is frozen out by the fixed boundary
condition.