Short-time scaling behavior of growing interfaces

TL;DR

This paper investigates the early-time scaling behavior of growing interfaces using the KPZ equation and MBE models, confirming theoretical predictions with simulations and estimating critical exponents in higher dimensions.

Contribution

It provides a theoretical analysis of short-time scaling in interface growth and verifies predictions through Monte Carlo simulations, especially in 2+1 dimensions.

Findings

Analytical expressions for initial slip exponents in KPZ.

Confirmation of theory via Monte Carlo simulations in 1+1 dimensions.

Estimated dynamical exponent z in 2+1 dimensions.

Abstract

The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE). The scaling behavior of response and correlation functions is reminiscent of the ``initial slip'' behavior found in purely dissipative critical relaxation (model A) and critical relaxation with conserved order parameter (model B), respectively. Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 1+1 dimensions, for which z is known exactly, the analytical theory for the KPZ equation is confirmed by a Monte-Carlo simulation of a simple ballistic deposition model. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function.