  The spin structure in a magnetic dot, which is an example of a quantum
few-body system, is studied as a function of exchange coupling strength and dot
size with in the semiclassical approximation on a discrete lattice. As the
exchange coupli ng is decreased or the size is increased, the ground state
undergoes a phase cha nge from a single domain ferromagnet to a spin vortex.
The line separating these two phases has been calculated numerically for small
system sizes. %, and analytically for larger dots. The dipolar interaction has
been fully included in our calculations. Magnon frequencies in such a dot have
also been calculated in both phases by the linearized equation of motion
method. These results have also been reproduced f rom the Fourier transform of
the spin autocorrelation function. From the magnon Density Of States (DOS), it
is possible to identify the magnetic phase of the dot. Furthermore, the magnon
modes have been characterized for both the ferromagnetic and the vortex phase,
and the magnon instability mechanism leading to the vortex-ferro transition has
also been identified. The results can also be used to compute finite
temperature magnetization or vort icity of magnetic dots.
