Finite Size Scaling Analysis of the Anderson Transition

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 localisation and the Anderson model of localisation 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.

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

References in corpus (4)

• Anderson Transitions
• Critical exponent for the quantum Hall transition
• Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model
• Observation of multifractality in Anderson localization of ultrasound

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• Study of off-diagonal disorder using the typical medium dynamical cluster approximation
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• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Disorder effects in correlated topological insulators
• Study of multiband disordered systems using the typical medium dynamical cluster approximation
• Finite Cluster Typical Medium Theory for Disordered Electronic Systems
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• Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Critical scaling of polarization waves on a heterogeneous chain of resonators
• Mapping the Current-Current Correlation Function Near a Quantum Critical Point
• Critical exponent for the quantum spin Hall transition in Z_2 network model
• Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
• Influence of the spin-orbit interaction in the impurity-band states of n-doped semiconductors
• Silicon Donor Array as a Disordered One-Dimensional Electron Gas