The critical exponent of the localization length at the Anderson transition in 3D disordered systems is larger than 1

P. Cain; M. L. Ndawana; R. A. Römer; M. Schreiber

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The critical exponent of the localization length at the Anderson transition in 3D disordered systems is larger than 1

P. Cain·M. L. Ndawana·R. A. Römer·M. Schreiber

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Abstract

In a recent communication to the cond-mat archives, Suslov [cond-mat/0105325] severely criticizes a multitude of numerical results obtained by various groups for the critical exponent $ν$ of the localization length at the disorder-induced metal-insulator transition in the three-dimensional Anderson model of localization as ``entirely absurd'' and ``evident desinformation''. These claims are based on the observation that there still is a large disagreement between analytical, numerical and experimental results for the critical exponent. The author proposes, based on a ``simple procedure to deal with corrections to scaling'', that the numerical data support nu approx 1, whereas recent numerical papers find nu = 1.58 +/- 0.06. As we show here, these claims are entirely wrong. The proposed scheme does neither yield any improved accuracy when compared to the existing finite-size scaling methods, nor does it give nu approx 1 when applied to high-precision data. Rather, high-precision numerics with error epsilon approx 0.1% together with all available finite-size-scaling methods evidently produce a critical exponent nu approx 1.58.

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P. Cain, M. L. Ndawana, R. A. Römer, M. Schreiber. 2001-06-01. The critical exponent of the localization length at the Anderson transition in 3D disordered systems is larger than 1. https://arxiv.org/abs/cond-mat/0106005

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