Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field [rapid communication]
Abstract
Using a fact that the effective conductivity σ of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for σ of isotropic heterophase systems are found. As known, for binary ( N=2) systems a determination of exact values of both conductivities (diagonal σ and transverse Hall σ) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase ( N⩾3) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and some phase concentrations are pairwise equal. In all these cases σ does not depend on phase concentrations. The complete, 3parametric, explicit transformation, connecting σ in binary systems with a magnetic field and without it, is constructed.
 Publication:

Physics Letters A
 Pub Date:
 March 2005
 DOI:
 10.1016/j.physleta.2004.12.084
 arXiv:
 arXiv:condmat/0412365
 Bibcode:
 2005PhLA..336..223B
 Keywords:

 75.70.Ak;
 72.80.Ng;
 72.80.Tm;
 73.61.r;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 3 figures, Latex2e