Symmetry based determination of space-time functions in nonequilibrium growth processes

TL;DR

This paper derives universal scaling functions for space-time correlation and response in nonequilibrium growth processes using symmetry principles, and confirms their applicability through atomistic models in different dimensions.

Contribution

It introduces a symmetry-based method to determine universal functions in nonequilibrium growth, correcting previous classifications of model universality classes.

Findings

Derived universal scaling functions from symmetry considerations.

Confirmed models belong to a single universality class in 1+1 and 2+1 dimensions.

Corrected earlier claims about different universality classes in 2+1 dimensions.

Abstract

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.