TY - JOUR

T1 - Surface roughening with quenched disorder in high dimensions

T2 - Exact results for the Cayley tree

AU - Buldyrev, Sergey V.

AU - Havlin, Shlomo

AU - Kertész, Janos

AU - Sadr-Lahijany, Reza

AU - Shehter, Arkady

AU - Stanley, H. Eugene

PY - 1995

Y1 - 1995

N2 - Discrete models describing pinning of a growing self-affine interface due to geometrical hindrances can be mapped to the diode-resistor percolation problem in all dimensions. We present the solution of this percolation problem on the Cayley tree. We find that the order parameter P varies near the critical point pc as exp(-A/ pc-p), where p is the fraction of bonds occupied by diodes. This result suggests that the critical exponent βp of P diverges for d→, and that there is no finite upper critical dimension. The exponent ν characterizing the parallel correlation length changes its value from ν=3/4 below pc to ν=1/4 above pc. Other critical exponents of the diode-resistor problem on the Cayley tree are γ=0 and ν=0, suggesting that ν/ν→0 when d→. Simulation results in finite dimensions 2≤d≤5 are also presented.

AB - Discrete models describing pinning of a growing self-affine interface due to geometrical hindrances can be mapped to the diode-resistor percolation problem in all dimensions. We present the solution of this percolation problem on the Cayley tree. We find that the order parameter P varies near the critical point pc as exp(-A/ pc-p), where p is the fraction of bonds occupied by diodes. This result suggests that the critical exponent βp of P diverges for d→, and that there is no finite upper critical dimension. The exponent ν characterizing the parallel correlation length changes its value from ν=3/4 below pc to ν=1/4 above pc. Other critical exponents of the diode-resistor problem on the Cayley tree are γ=0 and ν=0, suggesting that ν/ν→0 when d→. Simulation results in finite dimensions 2≤d≤5 are also presented.

UR - http://www.scopus.com/inward/record.url?scp=0006691020&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.52.373

DO - 10.1103/PhysRevE.52.373

M3 - Article

AN - SCOPUS:0006691020

SN - 1063-651X

VL - 52

SP - 373

EP - 388

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 1

ER -