Abstract
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 varies near the critical point as exp(-A/ √-p ), where p is the fraction of bonds occupied by diodes. This result suggests that the critical exponent of diverges for d→∞, and that there is no finite upper critical dimension. The exponent characterizing the parallel correlation length changes its value from =3/4 below to =1/4 above . Other critical exponents of the diode-resistor problem on the Cayley tree are γ=0 and =0, suggesting that /→0 when d→∞. Simulation results in finite dimensions 2≤d≤5 are also presented.
- Received 21 February 1995
DOI:https://doi.org/10.1103/PhysRevE.52.373
©1995 American Physical Society