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

TL;DR

This paper critically compares Monte Carlo simulations and a two-step approach for magnetic properties in dilute spin systems, revealing significant numerical shortcomings in existing MC results and emphasizing the need for improved large-scale calculations.

Contribution

The study identifies key numerical issues in recent Monte Carlo results and demonstrates the effectiveness of the TSA method in analyzing dilute magnetic systems.

Findings

Monte Carlo results suffer from large finite size effects

Statistical sampling in MC was insufficient for accurate results

Determination of Curie temperature in MC was too approximate

Abstract

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.