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Roughly half of numerical investigations of the Anderson transition are basedon consideration of an associated quasi-1D system and postulation ofone-parameter scaling for the minimal Lyapunov exponent. If this algorithm istaken seriously, it leads to unumbiguous prediction of the 2D phase transition.The transition is of the Kosterlitz-Thouless type and occurs betweenexponential and power law localization (Pichard and Sarma, 1981). Thisconclusion does not contradict numerical results if the raw data areconsidered. As for interpretation of these data in terms of one-parameterscaling, such interpretation is inadmissible: the minimal Lyapunov exponentdoes not obey any scaling. A scaling relation is valid not for minimal, but forsome effective Lyapunov exponent, whose dependence on parameters is determinedby scaling itself. If finite-size scaling is based on the effective Lyapunovexponent, existence of the 2D transition becomes not definite, but still ratherprobable. Interpretation of the results in terms of the Gell-Mann -- Lowequation is also given.Comment: PDF, 15 page

Analytical realization of finite-size scaling for Anderson localization: Is there a transition in the 2D case?