Hw. Lee et D. Kim, UNIVERSAL MACROSCOPIC BACKGROUND FORMATION IN SURFACE SUPERROUGHENING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(3), 1997, pp. 2347-2350
We study a class of super-rough growth models whose structure :Factor
satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic
background spontaneously develops in the local surface profile, which
dominates the scaling of the local surface width and the height diffe
rence. The shape of the macroscopic background takes a form of a finit
e-order polynomial whose order is decided from the value of the global
roughness exponent. Once the macroscopic background is subtracted, th
e width of the resulting local surface profile satisfies the Family-Vi
csek scaling. We show that this feature is universal to all super-roug
h growth models, and we also discuss the difference between the macros
copic background formation and the pattern formation in other models.