Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2011-04-03
J.Exp.Theor.Phys. 114, 107-117 (2012) [Zh.Eksp.Teor.Fiz. 141, 122-134 (2012) ]
Physics
Condensed Matter
Disordered Systems and Neural Networks
Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et al
Scientific paper
Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.
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