Scaling in a simple model for surface growth in a random medium
Amnon Aharony, Dietrich Stauffer
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 ∞, where the surface grows at the site with minimal random number, 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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