Effective conductivity of 2D isotropic two-phase systems in magnetic field

Using the linear fractional transformation, connecting effective conductivities $\widehat \sigma_{e}$ of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for $\widehat\sigma_{e}$ in a magnetic field are obtained. They allow to describe $\widehat \sigma_{e}$ of various inhomogeneous media at arbitrary phase concentration x and magnetic fields. The x-dependence plots of $\widehat\sigma_{e}$ at some values of inhomogeneity and magnetic field are constructed. Their behaviour is qualitatively compatible with the existing experimental data. The obtained results are applicable to different two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and admit a direct experimental checking.