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