Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} 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 sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) 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 the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructe

Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

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.Comment: 10 pages, Latex2e, 3 figure

Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} 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 sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) 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 the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructedComment: 15 pages, 3 figures, Latex2

Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

Explicit expressions for magnetoresistance $R$ of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations $x$ and magnetic fields $H$. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the $x$- and $H$-dependencies of $R(x,H)$ are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides $Ag_{2+\delta}Se.$ A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures.Comment: 12 pages, 2 figures, Latex2

The Misfit Strain Critical Point in the 3D Phase Diagrams of Cuprates

At the time of writing, data have been reported on several hundred different cuprates materials, of which a substantial fraction show superconductivity at temperatures as high as 130 K. The existence of several competing phases with comparable energy shows up in different ways in different materials, therefore it has not been possible to converge toward a universal theory for high Tc superconductivity. With the aim to find a unified description the Aeppli-Bianconi 3D phase diagram of cuprates has been proposed where the superlattice misfit strain (eta) is the third variable beyond doping (delta) and temperature T. The 3D phase diagrams for the magnetic order, and for the superconducting order extended to all cuprates families are described. We propose a formula able to describe the Tc (delta,eta) surface, this permits to identify the stripe quantum critical point at (delta)c=1/8 and (eta)c =7percent which is associated with the incommensurate to commensurate stripe phase transition, controlled by the misfit strain.Comment: 12 pages and 2 figure

Harmonic map analysis of SU(N) gravitating skyrmions

In this paper the SU(N) Einstein-Skyrme system is considered. We express the chiral field [which is not a simple embedding of the SU(2) field] in terms of harmonic maps. In this way, SU(N) spherical symmetric equations can be obtained easily for any N and the gravitating Skyrmion solutions of these equations can be studied. In particular, the SU(3) case is considered in detail and three different types of gravitating Skyrmions with topological charge four, two, and zero, respectively, are constructed numerically. Note that the configuration with zero topological charge corresponds to mixtures of Skyrmions and anti-Skyrmions