In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with lateral sizes $L_y>L_x$. Here, we extend this study to other universality classes for interface growth—specifically, the Edwards-Wilkinson (EW), the Mullins-Herring (MH), and the Villain-Lai-Das Sarma (VLDS) classes. From extensive simulations, we demonstrate that, in all systems with sufficiently large aspect ratio $\mathcal{R}=L_y/L_x$, the roughness $W$ scales with time $t$ in the growth regime as $W\sim t^{{\beta }_{\text{2D}}}$ for $t\ll t_c$ and $W\sim t^{{\beta }_{\text{1D}}}$ for $t\gg t_c$, where $t_c\sim L_x^{z_{2\text{D}}}$ in most cases. For the VLDS class, this crossover is also observed in the height distribution (HD), which approaches its characteristic probability density function for the 2D case at short times ($t\ll t_c$) and then crosses over to the asymptotic 1D HD. Dimensional crossovers are also found in the steady-state regime, both in the roughness scaling and in the VLDS HD, which interpolate between the 2D and 1D ones as $\mathcal{R}$ increases. The particular case $L_x=L_y^{\delta }$, with $0<\delta <1$, is also discussed in detail and reveals interesting features of the investigated systems. For instance, there exists a “special” exponent ${\delta }^{*}=z_{1\text{D}}/z_{2\text{D}}$ such that the temporal crossover cannot be observed for $\delta >{\delta }^{*}$. Moreover, this leads the saturation roughness to display a nonuniversal scaling, $W_s\sim L_y^{\mathrm{\Lambda }}$, with $\mathrm{\Lambda }=(1-\delta ){\alpha }_{1\text{D}}+\delta {\alpha }_{2\text{D}}$.

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• Ballistic deposition
• Growth processes
• Nonequilibrium systems
• Surface growth
• Kardar–Parisi–Zhang equation
• Monte Carlo methods
• Scaling methods