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

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We study a depinning transition of a discrete interface growthmodel for quenched impurities with an external driving forceF ind = 2 + 1 dimensions, and determine various critical exponents related to the depinning transition. At the critical forceFc, the growthvelocity v of the average interface height follows a power-law behaviorv(t) ∼ t − δ withδ≈0.460 and the interfacewidth W shows ascaling 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 velocityvs of the average interfaceheight shows vs ∼ (F − Fc)θ with θ≈0.575 for F > Fc. The lateral correlation length follows a power lawξr ∼ |F − Fc| − νr withνr≈0.71(3) and thecorrelation time τ ∼ |F − Fc| − νt with νt≈1.25(5). These exponents are very similar to those of directed percolation universality class.