On Effective Conductivity on ${\mathbb Z}^d$ Lattice

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dc.creatorFel, Leonid G.
dc.creatorKhanin, Konstantin M.
dc.date2001-11-30
dc.date2003-01-07
dc.date.accessioned2026-07-07T04:28:47Z
dc.date.available2026-07-07T04:28:47Z
dc.descriptionWe study the effective conductivity $σ_e$ for a random wire problem on the $d$-dimensional cubic lattice ${\mathbb Z}^d, d \geq 2$ in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0111048
dc.identifierhttp://arxiv.org/abs/math-ph/0111048
dc.identifierJ. Stat. Phys., {\bf 108}, N 5/6, 1015 -- 1031 (2002)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56924
dc.subjectMathematical Physics
dc.titleOn Effective Conductivity on ${\mathbb Z}^d$ Lattice
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