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Infinite face-centered-cubic network of identical resistors: Application to lattice Green’s function

Abstract

The equivalent resistance between the origin and any other lattice site, in an infinite face-centered-cubic network consisting of identical resistors, has been expressed rationally in terms of the known value \( f_o(3;0,0,0)\) and \( \pi\) . The asymptotic behavior is investigated, and some calculated values for the equivalent resistance are presented.

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Asad, J.H., Diab, A.A., Hijjawi, R.S. et al. Infinite face-centered-cubic network of identical resistors: Application to lattice Green’s function. Eur. Phys. J. Plus 128, 2 (2013). https://doi.org/10.1140/epjp/i2013-13002-8

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Keywords

  • Lattice Site
  • Recurrence Formula
  • Equivalent Resistance
  • Complete Elliptic Integral
  • Random Walk Method