Depinning transition of the quenched Kardar-Parisi-Zhang equation

Abstract

We study the pinning-depinning transition of the Kardar-Parisi-Zhang equation with quenched noise. We integrate the equation numerically and apply the finite-sizo scaling method to determine the critical exponents more accurately. At the critical force, the surface width W shows a scaling W(L,t) similar to L(alpha)f(t/L-z) with alpha = 0.633(8), beta = 0.647(2), and z = 0.978, where L is the system size. Near the critical force, the steady-state velocity v(s) follows v(s) similar to (F - F-c)(theta) with theta = 0.616(9). We find various other critical exponents related to the depinning transition through the finite-size scaling formulas of the velocity v. There are three independent exponents alpha, beta, and theta, and the other critical exponents are determined through them.