Dilute instanton gas as the precursor to the integral quantum Hall effect

An explicit expression is proposed for the renormalization-group equations for ${\sigma }_{\mathrm{xx}}$, ${\sigma }_{\mathrm{xy}}$, i.e., the magnetoconductance tensor for the two-dimensional disordered electronic system subject to a magnetic background field. The formulas are derived from the ‘‘dilute instanton gas’’ approximation, which is given a clear meaning within the previously derived nonlinear σ-model description for the transport properties of the system.