Kardar-Parisi-Zhang universality class in (2+1) dimensions: universal geometry-dependent distributions and finite-time corrections.

ABSTRACT

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t(-ß), where ß is the growth exponent. Our results support a generalization of the ansatz h=v(∞)t+(Γt)(ß)χ+η+ζt(-ß) to higher dimensions, where v(∞), Γ, ζ, and η are nonuniversal quantities whereas ß and χ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ class in two-dimensional systems.