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

DOI10.1088/0305-4470/33/42/103zbMATH Open0970.82018arXivcond-mat/9907413OpenAlexW3124574037MaRDI QIDQ2703505

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Publication date: 5 March 2001

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

Full work available at URL: https://arxiv.org/abs/cond-mat/9907413

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