Interface growth in high-dimensional disordered systems
Chemical Physics Department, Weizmann Institute of Science,
Rehovot, 76100 Israel
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