FINITE SIZE SCALING ANALYSIS OF THE ANDERSON TRANSITION

2010/04/02 by B. Krämer, Bernhard Kramer, A. MacKinnon +3
Chemistry · Mathematics · Physics and Astronomy · #Anderson localization #Chemistry #Condensed matter physics #Critical exponent #Geometry #Mathematics #Physics #Quantum and electron transport phenomena #Scaling #Scaling law #Spectroscopy and Quantum Chemical Studies #Statistical physics #Symmetry (geometry) #Theoretical and Computational Physics #Theoretical physics #Transition (genetics) #Widom scaling #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1142/s0217979210064630

12 pages, 1 figure. "Fifty Years of Anderson localization", edited by E. Abrahams (World Scientific, Singapore, 2010)

arxiv created 2010/04/02 · openalex publication_date 2010/05/20 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localization and the Anderson model of localization are briefly sketched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.

Citations

• Oscillatory effects and the magnetic susceptibility of carriers in inversion layers
• The theory of impurity conduction
• Spin-Orbit Coupling Effects in Zinc Blende Structures
• Scaling of the Conductivity with Temperature and Uniaxial Stress in Si:B at the Metal-Insulator Transition
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
• Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
• The Anderson Transition: Time Reversal Symmetry and Universality