Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections

TL;DR

This study explores the KPZ universality class in 2+1 dimensions through extensive simulations, revealing geometry-dependent universal distributions, finite-time corrections, and proposing a generalized scaling ansatz applicable to higher dimensions.

Contribution

It introduces the first detailed analysis of geometry-dependent distributions and finite-time corrections in 2+1D KPZ models, extending the universality framework beyond 1D.

Findings

Discovery of geometry-dependent universal distributions in 2+1D

Finite-time corrections characterized by a mean shift decaying as t^-eta

Generalized scaling ansatz supported for higher dimensions

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^-\beta, where \beta is the growth exponent. Our results support a generalization of the ansatz h = v t + (\Gamma t)^\beta \chi + \eta + \zeta t^-\beta to higher dimensions, where v, \Gamma, \zeta and \eta are non-universal quantities whereas \beta and \chi 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 KPZ class in two-dimensional systems.