Universality and geometry dependence in the class of the nonlinear molecular beam epitaxy equation

I. S. S. Carrasco, T. J. Oliveira

Published 2016-06-20Version 1

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, with flat and curved geometries. In both $d=1+1$ and $2+1$, we find that growth regime height distributions (HDs), spatial and temporal covariances are universal, but geometry-dependent, while the critical exponents are the same for flat and curved interfaces. Therefore the nMBE class does split into subclasses, as also does the Kardar-Parisi-Zhang (KPZ) class. Applying the "KPZ ansatz" to nMBE models, we estimate the cumulants of the $1+1$ HDs. Spatial covariance for flat subclass is hallmarked by a minima, which is not present in the curved one. Temporal correlations are shown to decay following well-known conjectures.