Pellegrini YP, Barthelemy M. Self-consistent effective-medium approximations with path integrals.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000;
61:3547-3558. [PMID:
11088131 DOI:
10.1103/physreve.61.3547]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/1999] [Revised: 12/17/1999] [Indexed: 05/23/2023]
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.
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