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Numerical calculations of the critical exponent of the localization length in the Chalker-Coddington (CC) model (\nu ~2.6) differ considerably from the experimental value (\nu~ 2.38) at the integer quantum Hall transition (IQHT). We review most of models considered recently, revile the origin of differences and the physics behind. The difference comes from the fact, that in CC model disorder of potential is not fully taken into account. Besides the phase factor disorder, coming from Bohm-Aharonov phase in the magnetic field, there is a structural disorder, connected with randomness of the position of saddle points of the random potential. At this points quantum tunneling is happening between Fermi lakes of the electrons in the potential landscape, which leads to change of localization length index \nu . We suggest, that interaction between electrons and atoms at the lattice sites affect disorder character of potential and, at the quasiclassical limit, on addition to U(1) phase disorder of CC model we have effective one particle random network model with structural disorder . In paper PRB.95, 125414 (2017) we propose a model for structural disorder, where numerical simulation on the basis of transfer matrix approach give a value \nu = 2.37 \pm 0.017, very close to the experimental value. Currently we have developed new technique of calculations and have launched new simulations of \nu based on S-matrix approach. Preliminary results confirm correctness of the value obtained earlier on basis of transfer matrix approach. We discuss also the role and validity of Harris criteria in a presence of structural disorder and argue, that the criteria should be modified.

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Ara Sedrakyan, Alikhanyan Natonal Science Laboratory, Yerevan, Armenia
Seminar Room 0.03, ETP
Contact: Alexander Altland