A Renormalization Group Approach for Randomly Distributed Conductance | Zendy

Kazakov V. A. | Zendy; Satanin A. M. | Zendy

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A Renormalization Group Approach for Randomly Distributed Conductance

Author(s) -

Kazakov V. A.,

Satanin A. M.

Publication year - 1981

Publication title -

physica status solidi (b)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.51

H-Index - 109

eISSN - 1521-3951

pISSN - 0370-1972

DOI - 10.1002/pssb.2221080103

Subject(s) - renormalization group , scaling , mathematics , conductance , lattice (music) , recursion (computer science) , percolation (cognitive psychology) , homogeneous , fixed point , percolation threshold , statistical physics , mathematical physics , physics , mathematical analysis , condensed matter physics , combinatorics , quantum mechanics , electrical resistivity and conductivity , geometry , algorithm , neuroscience , acoustics , biology

The recursion equation for the probability scaling behaviour of conductance for a randomly inhomogeneous resistive medium is obtained. The equation enables one to calculate percolation thresholds and a complete set of critical indices in the continuous percolation problem for which in a d ‐dimensional space the following formulae are derived: t = v ( d − 1), q = v , s = ( d − 1)/ d , m = ( dv ) −1 . For the cubic lattice t = 1.23 in a two‐dimensional and t = 1.74 in a three‐dimensional space are obtained. The scaling behaviour of dispersion and of the mean value of the normal distribution near a homogeneous fixed point is found.

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