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

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 < ν< 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.

4 pages, 2 figures