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.
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