Exact Results for Conductivity of 2D Isotropic Heterophase Systems

Details Exact Results for Conductivity of 2D Isotropic Heterophase Systems Exact Results for Conductivity of 2D Isotropic Heterophase Systems

2003-03-31

arxiv.org/abs/cond-mat/0303622v3

Phys.Lett. A, 313 (2003) 144 - 151

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, latex-2e, 2 figures, small corrections and reference are added

Scientific paper

10.1016/S0375-9601(03)00729-1

The duality relation for the effective conductivity sigma_{e} of 2D isotropic heterophase systems is used for obtaining the exact results for sigma_{e} at arbitrary number of phases N. The exact values of sigma_{e} correspond to the fixed points of the duality transformations. The new exact results for sigma_{e}, generalizing the well-known exact values of sigma_{e} for N = 2,3 at equal phase concentrations, are found. It is shown that for N > 3 there exist the whole hyperplanes in the space of phase concentrations, on which sigma_{e} takes constant values. These results are checked in the framework of various approximations for different random heterophase systems.

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