Volume 51, Number 5, September I 2000
|Page(s)||539 - 545|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 September 2002|
Master operators govern multifractality in percolation
Institut für Theoretische Physik
III, Heinrich-Heine-Universität Universitätsstraße 1, 40225
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.