DYNAMICS OF PARTICLE DEPOSITION ON A DISORDERED SUBSTRATE .1. NEAR-EQUILIBRIUM BEHAVIOR

A growth model that describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Siggia, and Rose formalism [Phys. Rev. A 8, 423 (1973)]. The periodic potential and the quenched disorder, upon averaging, are combined into a single term in the generating functional. Changing the temperature (or the inherent noise of the deposition process) two different regimes with a transition between them at Tsr are found: for T>Tsr this term is irrelevant and the surface has the scaling properties of a surface growing on a flat substrate in the rough phase. The height-height correlations behave as C(L,)ln[Lf(/L2)]. While the linear response mobility is finite in this phase it does vanish as (T-Tsr)1.78 when TTsr+. For T<Tsr there is a line of fixed points for the coupling constant. The surface is super-rough: the equilibrium correlation functions behave as (lnL)2 while their short time dependence is (ln)2 with a temperature-dependent dynamic exponent z=2[1+1.78(1-T/Tsr)]. While the linear response mobility vanishes on large length scales, its scale dependence leads to a nonlinear response. For a small applied force F the average velocity of the surface v behaves as vF1+. To first order =1.78(1-T/Tsr). At the transition, vF/(1+C-ln(F)-)1.78 and the crossover to the behavior to T<Tsr is analyzed. These results also apply to two-dimensional vortex glasses with a parallel magnetic field. © 1994 The American Physical Society.