A discrete interface growth model for quenched impurities in d=2+1 dimensions

Abstract

We study a depinning transition of a discrete interface growth model for quenched impurities with an external driving force F in d = 2 + 1 dimensions, and determine various critical exponents related to the depinning transition. At the critical force F(c), the growth velocity v of the average interface height follows a power-law behavior upsilon(t) similar to t(-delta) with delta approximate to 0.460 and the interface width W shows a scaling behavior W(2)(t, L) similar to L(2 alpha) f(t/L(z)) with alpha approximate to 1.02 and z approximate to 1.77 where L is the system size. The steady-state moving velocity vs of the average interface height shows upsilon(s) similar to (F - F(c))(theta) with theta approximate to 0.575 for F > F(c). The lateral correlation length follows a power law xi(r) similar to vertical bar F - F(c)vertical bar(-nu r) with nu(r) approximate to 0.71(3) and the correlation time t similar to vertical bar F - F(c)vertical bar(-nu t) with nu(t) approximate to 1.25(5). These exponents are very similar to those of directed percolation universality class.