Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface

TL;DR

This paper studies the geometric and statistical properties of iso-height lines in a 2D KPZ surface, revealing universal fractal behavior and conformal invariance in their contour lines.

Contribution

It provides new insights into the scaling and conformal invariance of iso-height lines in the 2D KPZ model, highlighting differences in cluster size distribution.

Findings

Height-cluster size distribution varies above and below mean height

Fractal dimensions of clusters and perimeters are unchanged

Contour lines exhibit conformal invariance consistent with self-avoiding walks

Abstract

We investigate the statistics of Iso-height lines of (2+1)-dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged. The winding angle statistics also confirms again the conformal invariance of these contour lines in the same universality class of self-avoiding random walks (SAWs).