Restricted curvature model on a tetrahedral fractal substrate

Abstract

We studied the restricted curvature model on a Sierpinski tetrahedral substrate under the restriction of the surface curvature. The interface width W grows as $t^{\beta }$ at the beginning and becomes saturated as $L^{\alpha }$ eventually for $L^{z} \ll t$ on a finite system of a lateral size L. We obtained $\beta = 0.307(9)$, $\alpha = 1.64(8)$, and $z \approx 5.34$, and these values are in good agreement with the power-counting predictions from a fractional Langevin equation, $\beta = \frac{1}{2} - d_{f} / 4z_\textrm{rw}$, $\alpha = z_\textrm{rw} -d_f / 2$, and $z=2z_\textrm{rw}$, where $d_f=2$ and $z_\textrm{rw} \approx 2.58$ are the fractal dimension of the Sierpinski tetrahedral substrate and the random walk exponent of the substrate, respectively. The relationship of the equilibrium restricted curvature model and the conserved restricted solid-on-solid model on fractal substrates is also discussed.