Strong coupling in conserved surface roughening: A new universality class?

TL;DR

This paper proposes that including an omitted nonlinear term in the conserved KPZ equation reveals a potential new universality class for surface growth, supported by theoretical divergence and numerical evidence in two dimensions.

Contribution

It identifies an overlooked nonlinear term in the conserved KPZ equation and demonstrates its impact on the universality class through renormalization group analysis and numerical simulations.

Findings

Divergence in 1-loop RG flow indicates a phase transition.

Numerical simulations in 2D show non-mean-field behavior.

Possible existence of a new universality class for surface growth.

Abstract

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This has non-mean-field behavior only in spatial dimension $d<2$. We point out here that cKPZ is incomplete: it omits a symmetry-allowed nonlinear gradient term of the same order as the one retained. Adding this term, we find a parameter regime where the $1$-loop renormalization group flow diverges. This suggests a phase transition to a new growth phase, possibly ruled by a strong coupling fixed point and thus described by a new universality class, for any $d>1$. In this phase, numerical integration of the model in $d=2$ gives clear evidence of non mean-field behavior.