Near-equilibrium dynamics of depinning transition of 1D crystalline interface in random environment

A 1D long-range interactive growth model which describes the deposition of particles on a disordered substrate is investigated. The stochastic growth equation was recast in terms of the Martin, Siggia, and Rose (MSR) action, with which the renormalization analysis is performed. By changing the temperature (or the inherent noise of the deposition process), two different regimes with a transition between them at Tpc, are found. For T> Tpc substrate disorder is irrelevant and the surface has the scaling properties of the surface growing on a flat substrate in a rough phase. The height-height correlations behave as C(L, τ) ln[Lƒ(τ/L)]. While the linear response mobility is finite in this phase it vanishes as (T − Tpcπ/2 when T → Tpc+. For T < Tpc, the flows of the coupling constant are driven toward a line of fixed points. The equilibrium correlations function behave still as (lnL) and short time dependence is (lnτ) with a temperature dependent dynamic exponent .