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

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

1999-07-27

arxiv.org/abs/cond-mat/9907413v2

J. Phys. A: Math. & Gen. 33 (2000) L393

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 2 figures

Scientific paper

10.1088/0305-4470/33/42/103

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.

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