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