Critical Discussion of the 2-Loop Calculations for the KPZ-Equation

TL;DR

This paper critically examines 2-loop calculations of the KPZ equation, clarifying discrepancies in critical exponents and confirming the absence of a strong-coupling fixed point at this order.

Contribution

It provides a detailed analysis of the renormalization procedure in 2-loop calculations, resolving inconsistencies and accurately determining critical exponents.

Findings

Correct critical exponents are zeta=O(epsilon^3) and z=2+O(epsilon^3) in d=2+epsilon.

No strong-coupling fixed point exists at 2-loop order.

Discrepancies between different groups' results are explained by renormalization issues.

Abstract

In this article, we perform a careful analysis of the renormalization procedure used in existing calculations to derive critical exponents for the KPZ-equation at 2-loop order. This analysis explains the discrepancies between the results of the different groups. The correct critical exponents in d=2+epsilon dimensions at the crossover between weak- and strong-coupling regime are zeta=O(epsilon^3) and z=2+O(epsilon^3). No strong-coupling fixed point exists at 2-loop order.