Review of recent progress on numerical studies of the Anderson transition

TL;DR

This paper reviews recent numerical studies of the Anderson transition in three-dimensional systems, highlighting precise estimates of critical exponents and boundary condition effects across different universality classes.

Contribution

It provides high-precision numerical estimates of the critical exponent for the Anderson transition and discusses boundary condition effects in different universality classes.

Findings

Critical exponent for orthogonal class: 1.57±0.02

Critical exponent for unitary class: 1.43±0.03

Boundary conditions influence transition properties

Abstract

A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent $\nu$ for the divergence of the localization length is estimated to be $\nu=1.57\pm 0.02$ for the orthogonal universality class, which is clearly distinguished from $\nu=1.43\pm 0.03$ for the unitary universality class. The boundary condition dependences of some quantities at the Anderson transition are also discussed.