Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

TL;DR

This study demonstrates that higher Lyapunov exponents in the three-dimensional Anderson model follow the same universal finite-size scaling as the smallest exponent, supporting one-parameter scaling of conductance distribution.

Contribution

It numerically proves the universal scaling behavior of higher Lyapunov exponents in the Anderson transition, extending previous finite-size scaling analyses.

Findings

Critical disorder Wc between 16.50 and 16.53

Critical exponent ν between 1.50 and 1.54

Validation of one-parameter scaling hypothesis

Abstract

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis of the one-parameter scaling of the conductance distribution. From the collected numerical data for quasi one dimensional systems up to the system size 24 x 24 x infinity we found the critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu < 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.