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

Using the linear fractional transformation, which connects the effective conductivities σ̂e of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for σ̂e in a magnetic field are obtained. They allow one to describe σ̂e of various inhomogeneous media at arbitrary phase concentrations x and magnetic fields. The x-dependence plots of σ̂e at some values of inhomogeneity and magnetic field are constructed. Their behavior is qualitatively compatible with the existing experimental data. The obtained results are applicable to different two-phase systems (regular and irregular as well as random), which satisfy the symmetry and self-duality conditions, and admit direct experimental checking.