The dynamics of a driven interface in a disordered medium close to the depinning threshold is analyzed. By a functional renormalization group scheme exponents characterizing the depinning transition are

Abstract. The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v N ( F -F,)' for driving forces F close to its threshold value F,. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical expo- Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold F,, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For E = I the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions E = 2,3 are larger and suggest that the roughness exponent is somewhat larger than the value [ = ~/ 3 of an interface in thermal equilibrium.

The order of magnitude of the typical distance ℓ between steps in MBE-grown crystal surfaces in calculated from simple scaling assumptions in the absence of evaporation. This distance is measurable by diffraction methods and yields access to the surface diffusion constant D. At the lowest non trivial temperatures the characteristic distance is of order (D/F)1/6 where F is the beam flux. At slightly higher temperature, ℓ is given by an algebraic formula which depends on the lifetime τ2 of a bound pair of adatoms at the surface, as well as of the diffusion constant D2 of these pairs. In certain ranges, ℓ varies as F-1/4 or F-1/5. At higher temperatures yet, ℓ is given by a formula which depends on a larger number of parameters. In special cases, our results are in agreement with the classical formulae of Stoyanov and Kashchiev, but disagree with certain recents works. ℓ is found to increase with temperature more rapidly than an Arrhenius exponential. Monte-Carlo simulations are reported and the discrepancy with certain other authors is clarified

No abstract

It isshown that the maximum density of islands in the submonolayer decreases approximately as a 1/3 -power of the bearn intensity F, in agreement with a prediction based on rate equations. A detailed analysis of adatom-adatom and adatom-island collisions explains some discrepancies between simulation data and simple rate-equation results.