We study the depinning transition of the quenched Mullins-Herring equation by direct integration method. At critical force $F_c$, the average surface velocity $v\left(t\right)$ follows a power-law behavior $v\left(t\right)\sim t^{-\delta }$ as a function of time $t$ with $\delta =0.160\left(5\right)$. The surface width has a scaling behavior with the roughness exponent $\alpha =1.50\left(6\right)$ and the growth exponent $\beta =0.841\left(5\right)$. Above the critical force, the steady state velocity $v_s$ follows $v_s\sim {(F-F_c)}^{\theta }$ with $\theta =0.289\left(8\right)$. Finite size scalings of the velocity are also discussed.

• Received 21 September 2005

DOI:https://doi.org/10.1103/PhysRevE.73.016140