The Upper Critical Dimension of the KPZ Equation

TL;DR

This paper investigates the upper critical dimension of the KPZ surface growth model, establishing it as less than or equal to four by analyzing directed polymers with quenched disorder.

Contribution

It provides a novel derivation of the upper critical dimension of the KPZ equation using a mapping to directed polymers with quenched disorder.

Findings

Upper critical dimension d_>  4 for KPZ

Bound state formation of coupled directed polymers below roughening temperature

Comparison of localization length singularities yields d_>  4

Abstract

The strong-coupling regime of Kardar-Parisi-Zhang surface growth driven by short-ranged noise has an upper critical dimension d_> less or equal to four (where the dynamic exponent z takes the value z (d_>) = 2). To derive this, we use the mapping onto directed polymers with quenched disorder. Two such polymers coupled by a small contact attraction are shown to form a bound state at all temperatures below the roughening temperature of a single polymer. Comparing the singularities of the localization length at and below the critical temperature yields d_> \leq 4.