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

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

2007-10-30

arxiv.org/abs/0710.5735v4

Physical Review B Volume 81, 224403 (2010)

Physics

Condensed Matter

Materials Science

11 pages, 9 figures

Scientific paper

10.1103/PhysRevB.81.224403

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}.

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