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. Zirnbauer (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 point’s 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 effective critical exponents ${\nu }_{\mathrm{eff}}$, which is necessarily dependent on the parameters of the model. We further support this idea by numerical determination of ${\nu }_{\mathrm{eff}}$ in suitably chosen models.

整数量子霍尔跃迁 (IQHT) 是安德森跃迁家族中最神秘的成员之一。自 1980 年代以来，IQHT 附近的标度行为在实验和数值模拟中得到了大力研究。尽管付出了一切努力，但众所周知，很难确定临界指数的精确值，这些指数似乎随模型细节而变化，从而挑战了普遍性原则。最近，M. Zirnbauer (2019) 推测了一个共形场理论的过渡，其中 β 函数中的线性项消失，导致固定点附近的流动非常缓慢，我们称之为边际缩放。在这项工作中，我们通过在前所未有的长度尺度上对 IQHT 的各种网络模型进行广泛的模拟，为这种情况提供了数值证据。危急时刻，我们表明，无序平均纵向兰道尔电导的有限大小缩放与其最近预测的定点值和 RG beta 函数的三阶扩展一致。将来，我们的数值结果可以用共形场理论的分析结果进行检查。远离临界性，我们描述了一种机制，可以解释一个有效临界指数${\nu }_{\mathrm{效果}}$，这必然取决于模型的参数。我们通过数值确定进一步支持这个想法${\nu }_{\mathrm{效果}}$ in suitably chosen models.