Interface growth in high-dimensional disordered systems

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 χ_c, and the second is the overall interface roughness. The overall roughness is generated by a combination of χ_c and the underlying interface dynamics. We predict the existence of a critical dimension above which χ_c 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.