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Self-Consistent Effective-Medium Approximations with Path Integrals

Yves-Patrick Pellegrini·Marc Barthelemy
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Abstract

We study effective-medium approximations for linear composite media by means of a path integral formalism with replicas. We show how to recover the Bruggeman and Hori-Yonezawa effective-medium formulas. Using a replica-coupling ansatz, these formulas are extended into new ones which have the same percolation thresholds as that of the Bethe lattice and Potts model of percolation, and critical exponents s=0 and t=2 in any space dimension d>= 2. Like the Bruggeman and Hori-Yonezawa formulas, the new formulas are exact to second order in the weak-contrast and dilute limits. The dimensional range of validity of the four effective-medium formulas is discussed, and it is argued that the new ones are of better relevance than the classical ones in dimensions d=3,4 for systems obeying the Nodes-Links-Blobs picture, such as random-resistor networks.

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BibTeXRIS

Yves-Patrick Pellegrini, Marc Barthelemy. 2000-01-17. Self-Consistent Effective-Medium Approximations with Path Integrals. https://doi.org/10.1103/physreve.61.3547

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