A driven growth model with quenched impurities on a sierpinski gasket substrate

Abstract

A discrete growth model with quenched impurities driven by an external force is studied on a Sierpinski gasket substrate. 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 ≈ 0.268(1), and the interface width W shows a scaling behavior W2(t,L) ∼ L2αf(t/Lz), with α ≈ 1.22(4) and z ≈ 1.68(4). Near Fc, the steady-state velocity scales as vs ∼ (F − Fc)θ, with θ ≈ 0.413(2). A possible fractional Langevin equation with quenched noise is introduced to describe the model.