Optimisation of multifractal analysis using box-size scaling

Abstract

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(alpha), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation. The typical and ensemble averaged scaling laws of the generalised inverse participation ratios are considered. In pursuit of a numerical optimisation of the box-scaling technique we discuss different box-partitioning schemes including cubic and non-cubic boxes, use of periodic boundary conditions to enlarge the system and single and multiple origins for the partitioning grid are also implemented. We show that the numerically most reliable method is to divide a system of linear size L equally into cubic boxes of size l for which L/l is an integer. This method is the least numerically expensive while having a good reliability.

6 pages, 4 figures

References in corpus (17)

• Multifractality and critical fluctuations at the Anderson transition
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Exact relations between multifractal exponents at the Anderson transition
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system
• A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Multifractal analysis of the metal-insulator transition in anisotropic systems
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Critical properties of the metal-insulator transition in anisotropic systems
• Scaling of the conductance distribution near the Anderson transition
• Review of recent progress on numerical studies of the Anderson transition
• Numerical investigations of scaling at the Anderson transition
• Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering

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• Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
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