  We study in this article properties of a nanodot embedded in a support by
Monte Carlo simulation. The nanodot is a piece of simple cubic lattice where
each site is occupied by a mobile Heisenberg spin which can move from one
lattice site to another under the effect of the temperature and its interaction
with neighbors. We take into account a short-range exchange interaction between
spins and a long-range dipolar interaction. We show that the ground-state
configuration is a vortex around the dot central axis: the spins on the dot
boundary lie in the $xy$ plane but go out of plane with a net perpendicular
magnetization at the dot center. Possible applications are discussed.
Finite-temperature properties are studied. We show the characteristics of the
surface melting and determine the energy, the diffusion coefficient and the
layer magnetizations as functions of temperature.
