Journal of Experimental and Theoretical Physics

, Volume 91, Issue 6, pp 1261–1267 | Cite as

A diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems

  • I. M. Khalatnikov
  • A. Yu. Kamenshchik
Solids Electronic Properties


The perturbation theory for calculating the ffective conductivity of the plane consisting of pieces of different conductivities is constructed, and a convenient diagram technique is elaborated for this perturbation theory. It is shown that for the chessboard, perturbative calculations give results that are in agreement with the well-known formula \(\sigma _{eff} = \sqrt {\sigma _1 \sigma _2 } \). The components of the effective conductivity tensor for the anisotropic three-color chessboard are calculated. It is shown that the isotropic (symmetric) part of the effective conductivity calculated up to the sixth order of perturbation theory satisfies the Bruggeman effective medium equation for symmetric three-color structures with equally partitioned components. We also consider an isotropic three-color chessboard with nonequal weights of colors. In this case, the perturbation theory in the fourth order contradicts the results following from the Bruggeman equation for nonequal weights.


Color Field Theory Elementary Particle Quantum Field Theory Perturbation Theory 
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Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • I. M. Khalatnikov
    • 1
    • 2
    • 3
  • A. Yu. Kamenshchik
    • 1
    • 2
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  2. 2.Landau Network-Centro VoltaComoItaly
  3. 3.School of Physics and Astronomy, Raymond and Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

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