Finite-size scaling from the self-consistent theory of localization
- P.L. Kapitza Institute for Physical Problems (Russian Federation)
Accepting the validity of Vollhardt and Woelfle's self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration 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 substantial 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{nu} of the correlation length, are explained by the fact that dependence L + L{sub 0} with L{sub 0} > 0 (L is the transversal size of the system) is interpreted as L{sup 1/{nu}} with {nu} > 1. The modified scaling relations are derived for dimensions d {>=} 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.
- OSTI ID:
- 22027941
- Journal Information:
- Journal of Experimental and Theoretical Physics, Vol. 114, Issue 1; Other Information: Copyright (c) 2012 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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