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Interpretation of high-dimensional numerical results for Anderson transition

Existence of the upper critical dimension d_{c2}=4 for the Anderson transition is a rigorous consequence of the Bogoliubov theorem on renormalizability of ϕ^4 theory. For dimensions d\ge 4, one-parameter scaling does not hold, and all existent numerical data should be reinterpreted. These data are exhausted by results for d=4,5 from scaling in quasi-one-dimensional systems, and results for d=4,5,6 from level statistics. All these data are compatible with the theoretical scaling dependencies obtained from self-consistent theory of localization by Vollhardt and Woelfle. The critical discussion is given for a widespread point of view that d_{c2}=\infty.