Short-time scaling behavior of growing interfaces

TL;DR

This paper investigates the early-stage scaling behavior of growing interfaces within the KPZ universality class, revealing connections to initial slip phenomena and estimating the dynamical exponent in 2+1 dimensions.

Contribution

It provides an analytical and numerical study of short-time scaling in KPZ interfaces, linking initial slip behavior to the dynamical exponent z.

Findings

Response and correlation functions show initial slip behavior similar to dissipative critical relaxation.

The initial slip exponent for KPZ can be expressed in terms of the dynamical exponent z.

Estimated z in 2+1 dimensions from short-time evolution of models.

Abstract

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip'' behavior found in purely dissipative critical relaxation (model A). Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function for ballistic deposition and for the RSOS model.