The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force F and temperature T. A continuous transition is found from a high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature-dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.
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