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The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical simulations. Despite all efforts, it is notoriously difficult to pin down the precise values of critical exponents, which seem to vary with model details and thus challenge the principle of universality. Recently, M. Zirnbauercitep{Zirnbauer2019} [Nucl. Phys. B textbf{941}, 458 (2019)] has conjectured a conformal field theory for the transition, in which linear terms in the beta-functions vanish, leading to a very slow flow in the fixed points vicinity which we term marginal scaling. In this work, we provide numerical evidence for such a scenario by using extensive simulations of various network models of the IQHT at unprecedented length scales. At criticality, we show that the finite-size scaling of the disorder averaged longitudinal Landauer conductance is consistent with its recently predicted fixed-point value and a third-order expansion of RG beta functions. In the future, our numerical findings can be checked with analytical results from the conformal field theory. Away from criticality we describe a mechanism that could account for the emergence of an emph{effective} critical exponents $ u_mathrm{eff}$, which is necessarily dependent on the parameters of the model. We further support this idea by numerical determination of $ u_mathrm{eff}$ in suitably chosen models.
Two-dimensional electron gas in the integer quantum Hall regime is investigated numerically by studying the dynamics of an electron hopping on a square lattice subject to a perpendicular magnetic field and random on-site energy with white noise distr
The puzzle of recently observed insulating phase of graphene at filling factor $ u=0$ in high magnetic field quantum Hall (QH) experiments is investigated. We show that the magnetic field driven Peierls-type lattice distortion (due to the Landau leve
The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a numerical Gre
We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known
We analyze the scaling behavior of the higher Lyapunov exponents at the Anderson transition. We estimate the critical exponent and verify its universality and that of the critical conductance distribution for box, Gaussian and Lorentzian distributions of the random potential.