Interface growth in high-dimensional disordered systems

O. Gat*, Z. Olami

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper presents a study of the dependence of the properties of interface growth in quenched disorder on space dimensionality. There are two independent roughness exponents in this problem. The first is the roughness of the invasion process χc, and the second is the overall interface roughness. The overall roughness is generated by a combination of χc and the underlying interface dynamics. We predict the existence of a critical dimension above which χc becomes 0 and the invasion clusters become fractal. This transition affects also the overall roughness, which identifies with the annealed roughness above the critical dimension. The high-dimensional behavior is demonstrated by analyzing the model on the Cayley tree. We find that the model on a Cayley tree is anomalous and fluctuation dominated. The theoretical scenario is supported by numerical simulations.

Original languageAmerican English
Pages (from-to)49-54
Number of pages6
JournalEurophysics Letters
Issue number1
StatePublished - 1 Oct 1996
Externally publishedYes


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