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

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

2002-01-04

arxiv.org/abs/cond-mat/0201043v1

Physics

Condensed Matter

Statistical Mechanics

11 pages including numerous figures; for Int. J. Mod. Phys. C

Scientific paper

10.1142/S0129183102003383

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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