Universal Coarsening and Giant-Cluster Formation in Growing Interfaces

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.