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Defects, Interface Profile and Phase Transitions in Growth Models

The effect of a localized defect on the profile of a one-dimensional growing surface is studied. It is found that the width of the average profile scales with the distance R from the defect as Rγ. A phase transition is observed as the velocity of propagation at the defect site is increased. For small velocities γ < 1, while above a critical value the profile becomes linear (γ = 1). This system provides a very interesting example of a phase transition in a one-dimensional probabilistic dynamical system.