Growth Shapes and Directed Percolation

Universal growth shape singularities are derived for a class of growth models which exhibit a kinetic roughening transition related to directed percolation. The curvature of the surface vanishes continuously at the transition point where the surface becomes anomalously flat. The shape close to a facet is determined by the fluctuations of the facet boundary. This implies a relation between d-dimensional directed percolation and (d − 1)-dimensional Edentype growth and leads to the exact result ν = 3/2 for the supercritical exponent of the angle-dependent correlation length in three-dimensional directed percolation.