| Issue |
Europhys. Lett.
Volume 36, Number 1, October 1996
|
|
|---|---|---|
| Page(s) | 49 - 54 | |
| Section | Condensed matter: structure, thermal and mechanical properties | |
| DOI | https://doi.org/10.1209/epl/i1996-00185-0 | |
| Published online | 01 September 2002 | |
Interface growth in high-dimensional disordered systems
Chemical Physics Department, Weizmann Institute of Science,
Rehovot, 76100 Israel
Received:
29
March
1996
Accepted:
22
August
1996
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 
, and the
second is the overall interface roughness. The overall roughness is
generated by a combination of and the underlying interface
dynamics. We
predict the existence of a critical dimension above which
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.
PACS: 64.60.Ht – Dynamic critical phenomena / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion
© EDP Sciences, 1996
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