Microstructure and Velocity of Field-Driven SOS Interfaces: Analytic Approximations and Numerical Results

TL;DR

This paper combines analytic mean-field theory and Monte Carlo simulations to study the structure and velocity of field-driven SOS interfaces in a 2D kinetic Ising model, revealing how the interface widens and speeds up with increasing field.

Contribution

It provides the first detailed comparison between analytic approximations and numerical simulations for the structure and dynamics of driven SOS interfaces.

Findings

Probability density width increases with field strength.

Excellent agreement between theory and simulation for interface velocity.

Increased correlations in step heights with stronger fields.

Abstract

The local structure of a solid-on-solid (SOS) interface in a two-dimensional kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field, is studied by an analytic mean-field, nonlinear-response theory [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field-dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.