# A tunable solid-on-solid model of surface growth - Condensed Matter > Statistical Mechanics

Abstract: We have performed a detailed Monte Carlo study of a diffusionless$1+1$-dimensional solid-on-solid model of particle deposition and evaporationthat not only tunes the roughness of an equilibrium surface but alsodemonstrates the need for more than two exponents to characterize it. Thetunable parameter, denoted by $\mu$, in this model is the dimensionless surfacetension per unit length. For $\mu < 0$, the surface becomes increasinglyspikier and its average width grows linearly with time; for $\mu = 0$, itswidth grows as $\sqrt{t}$. On the other hand, for positive $\mu$, the surfacewidth shows the standard scaling behavior, $\la \sigma mt a \simM^{\alpha}ft-M^{\alpha -\beta}$ where $M$ is the substrate size and $fx \toconst x^{\beta}$ for $x$ large small. The roughness exponent, $\alpha =1-2$ for $\mu \leq 2$, and $= 3-5, 4-5 and \sim 1$ for $\mu = 5, 6 and 7$respectively; the growth exponent, $\beta = 1-4$ for $\mu \leq 2$ and $= 1-2$for $\mu > \sim 3.5$ respectively. These exponents are different from those ofthe height-difference correlation function,$\alpha - = 1-2, \beta - = 1-4$ and$z- = 2$, for higher values of $\mu$ suggesting thereby that the surface couldbe self-constraining.

Author: S. L. Narasimhan, A. Baumgaertner

Source: https://arxiv.org/