Multifractality in directed percolation

Abstract

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.