On the reliability of recent Monte Carlo studies of dilute systems of localized spins interacting with itinerant carriers
Résumé
In this paper, we discuss the magnetic properties of dilute systems of localized spins interacting with itinerant carriers. More precisely, we compare recent available Monte Carlo (MC) results with our two-step-approach (TSA) calculations. The TSA depends first on the determination of the magnetic couplings and then on a proper treatment of the resulting effective dilute Heisenberg Hamiltonian. We show an important disagreement between the MC results (in principle exact) and our TSA calculations. We analyze the origins and shed light on the reasons for those dissensions. In contrast to what 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 MC simulations and TSA for the model study of the well-known III-V diluted magnetic semiconductor Ga1-xMn xAs. We hope that this work will motivate new systematic large-scale MC calculations.