Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-07-14
Phys. Rev. B 78, 195107 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
10 pages, 13 figures
Scientific paper
10.1103/PhysRevB.78.195107
We 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 $f(\alpha)$ 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 $f(\alpha)$ in the thermodynamic limit are also made.
Rodriguez Alberto
Roemer Rudolf A.
Vasquez Louella J.
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