LETTER TO THE EDITOR Exact exponent relations for random resistor-diode networks

Abstract. We investigate the percolation properties of a random network of non-directed bonds (resistors) and urbitrurily oriented directed bonds (diodes). For the square lattice, there is a multicritical line which connects the isotropic percolation threshold with a network fully occupied by randomly oriented diodes (‘random Manhattan’). Along this line, symmetry and invariance properties are used to demonstrate that the correlation length exponents are constant. Furthermore, a lattice independent relation is proved which shows that at the isotropic percolation threshold, the correlation length diverges with the same exponent when the transition is approached by varying either the resistor concentration or the concentration of randomly oriented diodes. Recently, there has been considerable attention devoted to directed percolation, a geometrical model in which directed bonds of a fixed orientation connect lattice sites (for a current review see e.g. Kinzel(l982)). Much of the interest in this model stems from its novel anisotropic critical behaviour. Applications of directed percolation include Reggeon field theory (Cardy and Sugar 1980) and branching Markov processes (Schlogl 1972) which arise in chemical reaction models