An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions

We solve exactly a special case of the anisotropic directed bond percolation problem in three dimensions, in which the occupation probability is 1 along two spatial directions, by mapping it to a five-vertex model. We determine the asymptotic shape of the ininite cluster and hence the direction dependent critical probability. The exponents characterising the fluctuations of the boundary of the wetted cluster in d-dimensions are related to those of the (d-2)-dimensional KPZ equation.