Ballistic deposition with power-law noise: A variant of the Zhang model

We study a variant of the Zhang model [Y.-C. Zhang, J. Phys. (Paris) 51, 2113 (1990)], ballistic deposition of rods with the length l of the rods being chosen from a power-law distribution P(l)∼${\mathit{l}}^{\mathrm{-}1\mathrm{-}\mathrm{\mu }}$. Unlike in the Zhang model, the site at which each rod is dropped is chosen randomly. We confirm that the growth of the rms surface width w with length scale L and time t is described by the scaling relation w(L,t)=${\mathit{L}}^{\mathrm{\alpha }}$w(t/${\mathit{L}}^{\mathrm{\alpha }/\mathrm{\beta }}$), and we calculate the values of the surface-roughening exponents α and β. We find evidence supporting the possibility of a critical value ${\mathrm{\mu }}_{\mathit{c}}$≊5 for d=1 with α=1/2 and β=1/3 for μ>${\mathrm{\mu }}_{\mathit{c}}$, while for μ<${\mathrm{\mu }}_{\mathit{c}}$, α and β vary smoothly, attaining the values α=β=1 for μ=2.