Weak pinning: surface growth in the presence of a defect

We study the influence of a point defect on the profile of a growing surface in the single-step growth model. We employ the mapping to the asymmetric exclusion model with blockage, and using Bethe-ansatz eigenfunctions as a starting approximation we are able to solve this problem analytically in two-particle sector. The dip caused by the defect is computed. A simple renormalization group-like argument enables to study scaling of the dip with increasing length of the sample L. For a horizontal surface we found that the surface is only weakly pinned at the inhomogeneity; the dip scales as a powerlaw Lγ with γ=0.58496. The value of the exponent agrees with direct numerical simulations of the inhomogeneous single-step growth model. In the case of tilted surfaces we observe a phase transition between weak and strong pinning and the exponent in the weak pinning regime depends on the tilt.