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 ones which have the same percolation thresholds as those of the Bethe lattice and Potts model of percolation, and critical exponents $s=0\mathrm{}$ and $t=2\mathrm{}$ in any space dimension $d>~2.$ Like the Bruggeman and Hori-Yonezawa formulas, the obtained 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 out formulas are of better relevance than the classical ones in dimensions $d=3,4\mathrm{}$ for systems obeying the nodes-links-blobs picture, such as random-resistor networks.

• Received 3 May 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3547