Critical behavior of diluted magnetic semiconductors: the apparent violation and the eventual restoration of the Harris criterion for all regimes of disorder

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the critical behavior of disordered Heisenberg models in diluted magnetic semiconductors, confirming the Harris criterion's applicability across all disorder regimes and clarifying apparent violations.

Contribution

It demonstrates that the Harris criterion holds for strongly disordered magnetic systems and clarifies the apparent violations by analyzing effective critical exponents near the transition.

Findings

Critical exponents agree with pure Heisenberg model predictions despite disorder.

Thermodynamic quantities self-average at the transition, with fluctuations diminishing as system size increases.

Apparent deviations in effective exponents near T_c are only transient and vanish very close to the critical temperature.

Abstract

Using large-scale Monte Carlo calculations, we consider strongly disordered Heisenberg models on a cubic lattice with missing sites (as in diluted magnetic semiconductors such as Ga_{1-x}Mn_{x}As). For disorder ranging from weak to strong levels of dilution, we identify Curie temperatures and calculate the critical exponents nu, gamma, eta, and beta finding, per the Harris criterion, good agreement with critical indices for the pure Heisenberg model where there is no disorder component. Moreover, we find that thermodynamic quantities (e.g. the second moment of the magnetization per spin) self average at the ferromagnetic transition temperature with relative fluctuations tending to zero with increasing system size. We directly calculate effective critical exponents for T > T_{c}, yielding values which may differ significantly from the critical indices for the pure system, especially in the presence of strong disorder. Ultimately, the difference is only apparent, and eventually disappears when T is very close to T_{c}.