disordered systems neural networks statistical mechanics
Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and allow to describe sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.
This is a pre-print. It is also available at: http://arxiv.org/abs/cond-mat/0504160. The definitive version in Physics Letters A, 337(4-6), pp. 449-456, is available at: http://www.sciencedirect.com/science/journal/03759601.