Quantized Scaling of Growing Surfaces

TL;DR

This paper uses exact field-theoretic methods to analyze the KPZ universality class of surface growth, deriving precise critical exponents for 2D and 3D surfaces based on assumed correlation properties.

Contribution

It provides exact values for the roughness and dynamic exponents in the KPZ class by applying a quantization condition derived from correlation assumptions.

Findings

Exact exponents for 2D surfaces: χ=2/5, z=8/5

Exact exponents for 3D surfaces: χ=2/7, z=12/7

Correlation properties differ from turbulent fluid correlations

Abstract

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness exponent $\chi$ and the dynamic exponent $z$. Hence the exact values $\chi = 2/5, z = 8/5$ for two-dimensional and $\chi = 2/7, z = 12/7$ for three-dimensional surfaces are derived.