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Scaling in a simple model for surface growth in a random medium

Amnon Aharony·Dietrich Stauffer
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Abstract

Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradient $m$ on the surface heights, and the latter by site-dependent random growth probabilities. Here we consider the limit $m \to \infty$, where the surface grows at the site with minimal random number, {\it independent} of its neighbors. The resulting height distribution obeys a simple scaling law, which is destroyed when local surface tension is included. Our model is equivalent to Yee's simplification of the Bak-Sneppen model for the extinction of biological species, where the height represents the number of times a biological species is exchanged.

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Amnon Aharony, Dietrich Stauffer. 2002-01-04. Scaling in a simple model for surface growth in a random medium. https://doi.org/10.1142/s0129183102003383

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