Dynamics of Toom interface in three dimensions

TL;DR

This paper introduces a new three-dimensional Toom model on a bcc lattice, analyzing its interface dynamics and showing it follows Edwards-Wilkinson and anisotropic KPZ equations under different conditions.

Contribution

It presents a novel 3D Toom model on a bcc lattice and derives its interface behavior, connecting it to well-known surface growth equations.

Findings

Surface width diverges logarithmically with space and time.

Model reduces to Edwards-Wilkinson equation in unbiased case.

Model reduces to anisotropic KPZ equation in biased case.

Abstract

We introduce a novel three dimensional Toom model on bcc lattice, and study its physical properties. In low-noise limit, the model leads to an effective solid-on-solid-type model, which exhibits a stationary interface via depositions and evaporations with avalanche process. We find that the model is described by the Edwards-Wilkinson equation for unbiased case and the anisotropic-Kardar-Parisi-Zhang equation in the weak-coupling limit for biased case. Thus the square of the surface width diverges logarithmically with space and time for both unbiased and biased cases.