We show, based on a direct numerical calculation of the Lyapunov exponents of the system and a finite-size single parameter scaling analysis, that the strong-field Landau level localization in a disordered two-dimensional electron gas is non-universal for short-range delta function random scatterers in the sense that the critical exponents in the two lowest Landau levels are substantially different. Inclusion of Landau level coupling and/or consideration of finite range of the random scattering potential in the theory restore the universality and make the computed critical exponents approximately equal.
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Liu et al. (1993) studied this question.