Interface fluctuations for deposition on enlarging flat substrates

TL;DR

This paper demonstrates that KPZ class models on expanding substrates exhibit curved-surface statistical properties, with universal height distributions and covariances, highlighting the significant role of substrate growth in interface fluctuation behavior.

Contribution

It reveals that expanding substrates induce KPZ curved subclass statistics even on flat interfaces, providing new insights into the influence of domain growth on universality classes.

Findings

Height distribution matches GUE Tracy-Widom in 1+1D

Spatial covariance aligns with Airy$_2$ process

Logarithmic correction due to duplication observed

Abstract

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In $1+1$ dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy$_2$ process, instead of the GOE and Airy$_1$ foreseen for flat interfaces. These results imply that, when the KPZ class splits into the curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in $2+1$ dimensions, the analogue of the GUE Tracy-Widom distribution for height distribution and that of the Airy$_2$ process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated to the duplication of column is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.