Dynamical Properties of a Growing Surface on a Random Substrate

TL;DR

This paper investigates the dynamics of a crystal surface on a disordered substrate using Monte Carlo simulations, revealing a phase transition from linear to nonlinear response influenced by temperature and driving force.

Contribution

It provides the first detailed numerical analysis of the surface dynamics, confirming theoretical predictions of a phase transition in response behavior.

Findings

Identified a continuous phase transition between response regimes.

Demonstrated agreement with dynamic renormalization group predictions.

Characterized the surface mobility as a function of temperature and driving force.

Abstract

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force $F$ and temperature $T$. A continuous transition is found from high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.