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

Amnon Aharony, Dietrich Stauffer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)603-612
Number of pages10
JournalInternational Journal of Modern Physics C
Issue number5
StatePublished - 1 Jun 2002
Externally publishedYes


  • Monte Carlo simulation
  • Surface growth

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Theory and Mathematics


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