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

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 Fc, the growth velocity v of the average interface height follows a power-law behavior v(t) ∼ t−δ with δ≈0.460 and the interface width W shows a scaling behavior W2(t, L) ∼ L2αf(t/Lz) with α≈1.02 and z≈1.77 where L is the system size. The steady-state moving velocity vs of the average interface height shows vs ∼ (F − Fc)θ with θ≈0.575 for F > Fc. The lateral correlation length follows a power law ξr ∼ |F − Fc|−νr with νr≈0.71(3) and the correlation time τ ∼ |F − Fc|−νt with νt≈1.25(5). These exponents are very similar to those of directed percolation universality class