Issue |
Europhys. Lett.
Volume 51, Number 5, September I 2000
|
|
---|---|---|
Page(s) | 539 - 545 | |
Section | Condensed matter: structure, mechanical and thermal properties | |
DOI | https://doi.org/10.1209/epl/i2000-00372-y | |
Published online | 01 September 2002 |
Master operators govern multifractality in percolation
Institut für Theoretische Physik
III, Heinrich-Heine-Universität Universitätsstraße 1, 40225
Düsseldorf, Germany
Received:
10
April
2000
Accepted:
7
July
2000
Using renormalization group methods, we study multifractality in percolation at the
instance of noisy random resistor networks. We introduce the concept of master operators.
The multifractal moments of the current distribution (which are proportional to the noise
cumulants of the resistance between two sites
x and
located on the same cluster) are related to such master operators. The scaling
behavior of the multifractal moments is governed exclusively by the master operators, even
though a myriad of servant operators is involved in the renormalization procedure. We
calculate the family of multifractal exponents
for the scaling
behavior of the noise cumulants,
, where ν is the correlation length exponent for
percolation, to two-loop order.
PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 72.70.+m – Noise processes and phenomena
© EDP Sciences, 2000
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