  We developed a technique to determine suitable spin models for small embedded
clusters of arbitrary geometry by combining the spin-cluster expansion with the
relativistic disordered local moment scheme. We present results for uncovered
and covered hexagonal Co clusters on Au(111) surface, and use classical Monte
Carlo simulations to study the temperature dependent properties of the systems.
To test the new method we compare the calculated spin-model parameters of the
uncovered clusters with those of a Co monolayer deposited on Au(111). In
general, the isotropic and DM interactions are larger between atoms at the
perimeter than at the center of the clusters. For Co clusters covered by Au,
both the contribution to the magnetic anisotropy and the easy axis direction of
the perimeter atoms differ from those of the inner atoms due to reduced
symmetry. We investigate the spin reversals of the covered clusters with
perpendicular magnetic anisotropy and by measuring the magnetization variance
in the easy direction we suggest a technique to determine the blocking
temperature of superparamagnetic particles. We also determine the N\'eel
relaxation time from the Monte Carlo simulations and find that it satisfies the
N\'eel--Arrhenius law with an energy barrier close to the magnetic anisotropy
energy of the clusters.
