Finite-time scaling for kinetic rough interfaces

TL;DR

This paper develops a finite-time scaling method to accurately determine critical exponents and universality classes of kinetic rough interfaces, validated through models with extremal dynamics and anisotropic variants.

Contribution

It introduces a finite-time scaling approach for kinetic rough interfaces, enabling precise estimation of critical exponents and classification into universality classes.

Findings

Isotropic model belongs to the same universality class as Sneppen model A.

Anisotropic model aligns with the universality class of the tensionless 1D KPZ equation.

Finite-time scaling effectively characterizes dynamic scaling and universality.

Abstract

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely characterize the underlying dynamics. We provide a finite-time scaling that systematically allows an estimation of the critical exponents and the scaling functions, eventually establishing the universality class accurately. As an illustration, we investigate a class of self-organized interface models in random media with extremal dynamics. The isotropic version shows a faceted pattern and belongs to the same universality class (as shown numerically) as the Sneppen (model A). We also introduce an anisotropic version of the Sneppen (model A) and suggest that the model belongs to the universality class of the tensionless one-dimensional Kardar-Parisi-Zhang equation.