  In magnetically-doped quantum dots changing the carrier occupancy, from open
to closed shells, leads to qualitatively different forms of carrier-mediated
magnetic ordering. While it is common to study such nanoscale magnets within a
mean field approximation, excluding the spin fluctuations can mask important
phenomena and lead to spurious thermodynamic phase transitions in small
magnetic systems. By employing coarse-grained, variational, and Monte Carlo
methods on singly and doubly occupied quantum dots to include spin
fluctuations, we evaluate the relevance of the mean field description and
distinguish different finite-size scaling in nanoscale magnets.
