Finite-size scaling of the level compressibility at the Anderson transition |
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Authors: | ML Ndawana RA Römer M Schreiber |
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Institution: | Institut für Physik, Technische Universit?t, 09107 Chemnitz, Germany, DE
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Abstract: | We compute the number level variance Σ
2 and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be
used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With
N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level
spacing, we find that both χ(N, W) and the integrated Σ
2 obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder
given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W
c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06
at the metal-insulator transition in very close agreement with previous results.
Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002 |
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Keywords: | PACS 71 30 +h Metal-insulator transitions and other electronic transitions – 71 23 An Theories and models localized states – 72 15 Rn Localization effects (Anderson or weak localization) |
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