Untitled

2002

Phys. Rev. E

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Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the non-percolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents {ψ l }. We calculate the family {ψ l } to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.

mentioning

confidence: 83%

“…[29,31]) to second order in ε. ψ 1 is in conformity with our result for the resistance exponent φ given in Refs. [29,32]. This has to be the case because C (1)…”

Section: (338)mentioning

confidence: 99%

Multifractal properties of resistor diode percolation

2002

Phys. Rev. E

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“…Our real-world interpretation [15,19,20,22,23,24,25,26,27], in which the conducting diagrams are viewed as being resistor networks themselves, provides for a powerful and elegant framework to calculate these diagrams. At first we rewrite the propagators in Schwinger parameterization,…”

Section: Review Of the Rrnmentioning

confidence: 99%

Conductivity of continuum percolating systems

2001

Phys. Rev. E

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We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be mapped onto a bond percolation model where the conductance sigma of randomly occupied bonds is drawn from a probability distribution of the form sigma(-a). Employing the methods of renormalized field theory we show to arbitrary order in epsilon expansion that the critical conductivity exponent of the Swiss-cheese model is given by t(SC)(a) = (d-2)nu + max[phi,(1-a)(-1)], where d is the spatial dimension and nu and phi denote the critical exponents for the percolation correlation length and resistance, respectively. Our result confirms a conjecture that is based on the "nodes, links, and blobs" picture of percolation clusters.

“…For details on deriving a field theoretic model for the RRDN we refer to Refs. [4,5]. In the vicinity of the transitions from the non-percolating to either of the directed percolating phases this model can be written in the form of a dynamic response functional [19,20,21],…”

Section: The Model Its Variants and The Physical Contentsmentioning

confidence: 99%

Transport properties of directed percolation clusters at the upper critical dimension

J. Phys.: Condens. Matter

2005

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We study the transport properties of directed percolation clusters at the upper critical dimension dc = 4 + 1, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field theory and renormalization group methods we calculate these logarithmic corrections up to and including the next to leading correction for a variety of observables, viz. the connectivity, i.e., the probability that two given points are connected, the average twopoint resistance and some of the fractal masses describing percolation clusters. Furthermore, we study logarithmic corrections for the multifractal moments of the current distribution on directed percolation clusters.