Multisurface coding simulations of the restricted solid-on-solid model in four dimensions

We study the restricted solid-on-solid model for surface growth in spatial dimension $d=4$ by means of a multisurface coding technique that allows us to analyze samples of size up to ${256}^4$ in the steady-state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that $d=4$ is not the upper critical dimension of the model.

Figure 1

Scaling plot of the rescaled second moment $w_2/\left[A_2{L}^{2\chi }(1+B_2{L}^{-\omega })\right]$ vs. the rescaled time $t/L^z$.

Figure 2

The quantities $w_2,$ $w_3$, $w_4$ are displayed as a function of $L$. Dots with error bars are values obtained by simulations, while solid lines are the eight-parameter best-fit reported in Ref. [13]. The vertical arrow arrow at $L=28$ represents the largest size simulated in Ref. [13].

Figure 3

Local slopes of $w_{2,3,4}$ are displayed as a function of $L^{-1}$. Dots with error bars are values obtained by simulations, while lines are the eight-parameter best-fit reported in Table . The solid horizontal line is at $\chi =0.2538$, i.e., the best-fit prediction for the wandering exponent.