  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.
