  Directed percolation is one of the generic universality classes for dynamic
processes. We study the crossover from isotropic to directed percolation by
representing the combined problem as a random cluster model, with a parameter
$r$ controlling the spontaneous birth of new forest fires. We obtain the exact
crossover exponent $y_{DP}=y_T-1$ at $r=1$ using Coulomb gas methods in 2D.
Isotropic percolation is stable, as is confirmed by numerical finite-size
scaling results. For $D \geq 3$, the stability seems to change. An intuitive
argument, however, suggests that directed percolation at $r=0$ is unstable and
that the scaling properties of forest fires at intermediate values of $r$ are
in the same universality class as isotropic percolation, not only in 2D, but in
all dimensions.
