Related Experiment Video
Updated: Jul 31, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
Published on: February 23, 2018
Self-consistent effective-medium approximations with path integrals
1Service de Physique de la Matiere Condensee, Commissariat a l'Energie Atomique, Boiinsertion markte Postale12, 91680 Bruyeres-le-Chainsertion marktel, France.
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 ones which have the same percolation thresholds as those 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 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 for systems obeying the nodes-links-blobs picture, such as random-resistor networks.
Related Concept Videos
Reaction Mechanisms: The Steady-State Approximation
Approximate Integration
The Midpoint Rule for Double Integrals
Change of Variables in Multiple Integrals
Substitutions in Multiple Integrals
The Fundamental Theorem for Line Integrals

