Roughness of two-dimensional surfaces with global constraints
Yup Kim, S. Y. Yoon · Physical Review E · 2005
We study dynamical scaling properties of the two-dimensional surface growth models with global constraints. These include the growth model from a partition function $Z={\ensuremath{\sum}}_{{h(\stackrel{P\vec}{r})}}{\ensuremath{\prod}}_{h={h}_{\mathit{min}}}^{{h}_{\mathit{max}}}\frac{1}{2}(1+{z}^{{n}_{h}})$, multiparticle-correlated surface growth models and dissociative $Q$-mer growth models. The equilibrium surfaces of all the models except the dimer model show the same dynamical scaling behavior ${W}^{2}(L,t)=(1∕2\ensuremath{\pi}{K}_{G})\mathrm{ln}[L\phantom{\rule{0.3em}{0ex}}g(t∕{L}^{{z}_{W}})]$ with ${z}_{W}=2.5$ and ${K}_{G}=0.916$, whereas the surface in the dimer model has a correction to the scaling. The growing (eroding) surfaces have two phases. The models with $z\ensuremath{\geqslant}0$ show the normal Kardar-Parisi-Zhang scaling behavior. In contrast the models with $\ensuremath{-}1\ensuremath{\leqslant}z<0$ and multiparticle-correlated growth model manifest grooved surface structures with $\ensuremath{\alpha}=1$. The growing surfaces of $Q$-mer models form rather complex facets.