Dimensional crossover in Kardar-Parisi-Zhang growth
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916233542107136 |
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| author | Carrasco, Ismael S. S. Oliveira, Tiago J. |
| author_facet | Carrasco, Ismael S. S. Oliveira, Tiago J. |
| contents | Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($ξ$) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates $L_x \neq L_y$ and, thus, the surfaces can become correlated in a single direction, when $ξ\sim L_x \ll L_y$. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as $W \sim t^{β_{\text{2D}}}$ for $t \ll t_c$ and $W \sim t^{β_{\text{1D}}}$ for $t \gg t_c$, where $t_c \sim L_x^{1/z_{2\text{D}}}$. The height distributions (HDs) also cross over from the 2D flat [cylindrical] HD to the asymptotic Tracy-Widom GOE [GUE] distribution. Moreover, 2D-to-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimensional crossover in Kardar-Parisi-Zhang growth Carrasco, Ismael S. S. Oliveira, Tiago J. Statistical Mechanics Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($ξ$) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates $L_x \neq L_y$ and, thus, the surfaces can become correlated in a single direction, when $ξ\sim L_x \ll L_y$. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as $W \sim t^{β_{\text{2D}}}$ for $t \ll t_c$ and $W \sim t^{β_{\text{1D}}}$ for $t \gg t_c$, where $t_c \sim L_x^{1/z_{2\text{D}}}$. The height distributions (HDs) also cross over from the 2D flat [cylindrical] HD to the asymptotic Tracy-Widom GOE [GUE] distribution. Moreover, 2D-to-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. |
| title | Dimensional crossover in Kardar-Parisi-Zhang growth |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2404.19516 |