Finite Size Scaling Analysis of the Anderson Transition

TL;DR

This paper reviews three decades of finite size scaling analysis of the Anderson transition, highlighting critical exponents, corrections to scaling, and comparisons with experimental data.

Contribution

It provides a comprehensive summary of recent results on critical exponents and emphasizes the importance of corrections to scaling in Anderson localization studies.

Findings

Critical exponents vary across symmetry classes

Corrections to scaling significantly affect results

Comparison with experiments shows good agreement

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.