Year: 2024
Type: article
Abstract: Two-dimensional (2D) Kardar-Parisi-Zhang (KPZ) growth is usually investigated on substrates of lateral sizes ${L}_{x}={L}_{y}$, so that ${L}_{x}$ and the correlation length ($\ensuremath{\xi}$) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates ${L}_{x}\ensuremath{\ne}{L}_{y}$ and, thus, the surfaces can become correlated in a single direction, when $\ensuremath{\xi}\ensuremath{\sim}{L}_{x}\ensuremath{\ll}{L}_{y}$. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as $W\ensuremath{\sim}{t}^{{\ensuremath{\beta}}_{\text{2D}}}$ for $t\ensuremath{\ll}{t}_{c}$ and $W\ensuremath{\sim}{t}^{{\ensuremath{\beta}}_{\text{1D}}}$ for $t\ensuremath{\gg}{t}_{c}$, where ${t}_{c}\ensuremath{\sim}{L}_{x}^{1/{z}_{2\text{D}}}$. The height distributions (HDs) also cross over from the 2D flat (cylindrical) HD to the asymptotic Tracy-Widom Gaussian orthogonal ensemble (Gaussian unitary ensemble) distribution. Moreover, 2D to one-dimensional (1D) crossovers are found also in the asymptotic growth velocity and in the steady-state regime of flat systems, where a family of universal HDs exists, interpolating between the 2D and 1D ones as ${L}_{y}/{L}_{x}$ increases. Importantly, the crossover scalings are fully determined and indicate a possible way to solve 2D KPZ models.
Source: Physical review. E
Authors: Ismael S. S. Carrasco, Tiago J. Oliveira
Institutions: Universidade de Brasília, Universidade Federal de Viçosa
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G266071807
OpenAlex ID: W4396510759