CROSSOVER FROM ISOTROPIC TO DIRECTED PERCOLATION

Directed percolation is one of the generic dynamic universality classe s. We study the crossover from isotropic to directed percolation by re presenting the combined problem as a random cluster model. A parameter r controls the spontaneous birth of new forest fires. We obtain the e xact crossover exponent y(DP) = y(T) - 1 at r = 1 using Coulomb gas me thods. Isotropic percolation is stable in 2D. Our numerical finite-siz e scaling results confirm this. An intuitive argument suggests that di rected percolation at r = 0 does not change stability for D greater th an or equal to 3. It remains unstable, such that forest fires at 0 < r < 1 have the same scaling properties as isotropic percolation all dim ensions.