  We have performed realistic atomistic simulations at finite temperatures
using Monte Carlo and atomistic spin dynamics simulations incorporating quantum
(Bose-Einstein) statistics. The description is much improved at low
temperatures compared to classical (Boltzmann) statistics normally used in
these kind of simulations, while at higher temperatures the classical
statistics are recovered. This corrected low-temperature description is
reflected in both magnetization and the magnetic specific heat, the latter
allowing for improved modeling of the magnetic contribution to free energies. A
central property in the method is the magnon density of states at finite
temperatures and we have compared several different implementations for
obtaining it. The method has no restrictions regarding chemical and magnetic
order of the considered materials. This is demonstrated by applying the method
to elemental ferromagnetic systems, including Fe and Ni, as well as Fe-Co
random alloys and the ferrimagnetic system GdFe$_3$ .
