Self-Consistent Effective-Medium Approximations with Path Integrals
摘要
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.
引用
@article{arxiv.cond-mat/0001223,
title = {Self-Consistent Effective-Medium Approximations with Path Integrals},
author = {Yves-Patrick Pellegrini and Marc Barthelemy},
journal= {arXiv preprint arXiv:cond-mat/0001223},
year = {2008}
}
备注
18 pages, 6 eps figures