Universal Coarsening and Giant-Cluster Formation in Growing Interfaces

TL;DR

This paper investigates the coarsening dynamics of clusters in 2D growing interfaces within the KPZ universality class, revealing universal scaling behaviors and the emergence of giant clusters.

Contribution

It uncovers universal scaling forms and the formation of giant clusters in the coarsening process of 2D growing interfaces, a previously unexplored phenomenon.

Findings

Statistical time invariance of cluster configurations

Shared scaling forms across different models

Emergence of a giant cluster exceeding correlation length

Abstract

Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood. Here, we numerically investigate this unexplored coarsening of clusters in 2D growing interfaces believed to belong to the Kardar-Parisi-Zhang universality class. Using a two-point spatial correlator, we demonstrate statistical time invariance of the evolving configurations and identify scaling forms shared across distinct models. We reveal a pronounced asymmetry in the growth of the largest clusters: one cluster emerges as a giant structure whose characteristic length exceeds the correlation length. Population-dependent scaling forms for the number densities of cluster areas are uncovered. These findings highlight new universal aspects of growing interfaces and suggest avenues for experimental verification.