Quantum corrections to conductivity under conditions of the integer quantum Hall effect

Quantum corrections to the conductivity of a two-dimensional electron gas under conditions of the integer quantum Hall effect have been studied. It is shown that violation of the one-parameter scaling under conditions of quantizing magnetic fields, $\omega_c\tau\gg$ 1, occurs at a level of the perturbation theory. The results of diagrammatic calculation of the quantum correction are in agreement with the numerical dependences of the peaks in the longitudinal conductivity on the effective size of the sample, in contrast to earlier calculations based on the unitary nonlinear $\sigma$-model. Due to this, consideration of Landau quantization represents a criterion for correct description of the quantum Hall effect.