Physics – Condensed Matter
Scientific paper
1994-10-10
Physics
Condensed Matter
19 pages, REVTEX, 5 figures upon request, INHA-PHYS-94-001
Scientific paper
10.1103/PhysRevE.51.1047
Surface structure of a restricted ballistic deposition(RBD) model is examined on a one-dimensional staircase with free boundary conditions. In this model, particles can be deposited only at the steps of the staircase. We set up recurrence relations for the surface fluctuation width $W$ using generating function method. Steady-state solutions are obtained exactly given system size $L$. In the infinite-size limit, $W$ diverges as $L^\alpha$ with the scaling exponent $\alpha=\frac{1}{2}$. The dynamic exponent $\beta$ $(W\sim t^\beta)$ is also found to be $\frac{1}{2}$ by solving the recurrence relations numerically. This model can be viewed as a simple variant of the model which belongs to the Kardar-Parisi-Zhang (KPZ) universality class $(\alpha_{KPZ}= \frac{1}{2} , \beta_{KPZ}=\frac{1}{3})$. Comparing its deposition time scale with that of the single-step model, we argue that $\beta$ must be the same as $\beta_{KPZ}/(1-\beta_{KPZ})$, which is consistent with our finding.
Ha Meesoon
Kim In-mook
Park Hyunggyu
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