A discrete model of the quenched Kardar-Parisi-Zhang equation

We introduce a discrete surface growth model to study the depinning transition of the quenched Kardar-Parisi-Zhang (QKPZ) equation with an external driving force F. At the critical force F, the surface width W shows a scaling W(t, L) similar to L-alpha f (t/L-z) with alpha approximate to 0.627, beta approximate to 0.617 and z approximate to 1.02. Near F-c, the steady-state velocity v(s) follows v(s) (F) similar to (F - F-c)(theta) with theta approximate to 0.672. From the finite-size scaling of the growth velocity, we obtain a correlation time exponent v(t) approximate to 1.781, a correlation height exponent vh = v(t)beta 1.099, and a correlation length exponent v(x) = v(t)/z approximate to 1.754 independently. V-h and v. are consistent with the values of the directed percolation (DP) class. Since the growing site is considered as an active site of the absorbing model, the interface pinning of the surface model is discussed in connection with the absorbing state.