An exactly solvable lattice model for inhomogeneous interface growth

We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact expressions for the average height and height fluctuations as functions of space and time for an initially flat interface. For a given defect strength there is a critical angle between the defect line and the growth direction above which a cusp in the interface develops. In the mapping to polymers in random media this is an example for the transverse Meissner effect. Fluctuations around the mean shape of the interface are Gaussian.