Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging

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dc.creatorRodriguez, Alberto
dc.creatorVasquez, Louella J.
dc.creatorRoemer, Rudolf A.
dc.date2008-07-14
dc.date.accessioned2026-07-07T10:17:21Z
dc.date.available2026-07-07T10:17:21Z
dc.descriptionWe study the multifractal analysis (MFA) of electronic wavefunctions at the localisation-delocalisation transition in the 3D Anderson model for very large system sizes up to $240^3$. The singularity spectrum $f(α)$ is numerically obtained using the \textsl{ensemble average} of the scaling law for the generalized inverse participation ratios $P_q$, employing box-size and system-size scaling. The validity of a recently reported symmetry law [Phys. Rev. Lett. 97, 046803 (2006)] for the multifractal spectrum is carefully analysed at the metal-insulator transition (MIT). The results are compared to those obtained using different approaches, in particular the typical average of the scaling law. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA. Some conjectures about the true shape of $f(α)$ in the thermodynamic limit are also made.
dc.description10 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/0807.2209
dc.identifierhttp://arxiv.org/abs/0807.2209
dc.identifierPhys. Rev. B 78, 195107 (2008)
dc.identifierdoi:10.1103/PhysRevB.78.195107
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173827
dc.subjectDisordered Systems and Neural Networks
dc.titleMultifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
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