Multifractality in directed percolation
Institut für Theoretische Physik III,
Accepted: 14 June 2001
Using renormalization group methods we study multifractality in directed percolation. Our approach is based on random lattice networks consisting of resistor-like and diode-like bonds with microscopic noise. These random resistor diode networks capture the features of isotropic as well as directed percolation. In this note we introduce a field-theoretic Hamiltonian for the multifractal properties at the transition from the non-percolating to the directed percolating phase. We investigate the multifractal moments of the current distribution and determine a family of critical exponents for these moments 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, 2001