A random rule model of surface growth

TL;DR

This paper introduces a modified surface growth model that uses sequential site scanning with rule-based randomness, improving the analysis of dynamic properties and computational efficiency.

Contribution

It presents a novel surface growth model with sequential scanning and rule-based randomness, reducing finite size effects and enabling parallel computation.

Findings

Reduces finite size effects and short-time anomalies.

Increases saturation time for surface growth.

Enhances computational efficiency and parallelization.

Abstract

Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random, substrate scan. The randomicity is introduced not in the site selection but in the choice of the rule to be followed in each site. The change positively affects the study of dynamic and asymptotic properties, by reducing the finite size ef- fect and the short-time anomaly and by increasing the saturation time. It also has computational benefits: better use of the cache memory and the possibility of parallel implementation.