Universality classes of the Kardar-Parisi-Zhang equation

TL;DR

This paper re-examines the mode-coupling theory for the KPZ equation, revealing two solution branches corresponding to different universality classes depending on spatial dimension, with implications for understanding surface growth phenomena.

Contribution

It identifies two distinct universality classes of the KPZ equation in different dimensions, extending the understanding of its strong coupling solutions.

Findings

Two solution branches exist for the KPZ equation.

One branch applies for dimensions less than 2, matching previous analytic results.

The second branch extends up to dimension 4, aligning with numerical studies.

Abstract

We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation in the strong coupling limit and show that there exists two branches of solutions. One branch (or universality class) only exists for dimensionalities $d<d_c=2$ and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to $d_c=4$ and gives values for the dynamical exponent $z$ similar to those of numerical studies for $d\ge2$.