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In this paper, we discuss magnetic properties of dilute systems of localizedspins interacting with itinerant carriers. More precisely, we compare recentavailable Monte Carlo results with our two step approach (TSA) calculations.The TSA consists first on the determination of the magnetic couplings and thenon a proper treatment of the resulting effective dilute Heisenberg Hamiltonian.We show important disagreement between the Monte Carlo results (in principleexact) and our TSA calculations. We analyze the origins and shed light on thereasons of those dissensions. In contrast to one could expect, we demonstratethat the available MC calculations suffer from severe numerical shortcomings.More precisely, (i) the finite size effects appear to be huge in dilutesystems, (ii) the statistical sampling (disorder configurations) was far toosmall, and (iii) the determination of the Curie temperature was too rough. Inaddition, we provide new arguments to explain a recent disagreement between theMonte Carlo simulations and TSA for the model study of the well known III-Vdiluted magnetic semiconductor Ga$_{1-x}$Mn$_{x}$As. We hope that this workwill motivate new systematic large scale Monte Carlo calculations.

On the reliability of recent Monte Carlo studies of dilute systems of localized spins interacting with itinerant carriers