DYNAMICS OF A TOOM INTERFACE IN 3 DIMENSIONS

Abstract

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