SURFACE ROUGHENING WITH QUENCHED DISORDER IN HIGH DIMENSIONS - EXACT RESULTS FOR THE CAYLEY TREE

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-infinity varies near the critical point p(c) as exp(-A/root p(c)-p), where p is the fraction of bonds occupied by diodes; This result suggests that the critical exponent beta(p) of P-infinity diverges for d --> infinity, and that there is no finite upper critical dimension. The exponent nu(parallel to) characterizing the parallel correlation length changes its value from nu(parallel to) = 3/4 below p(c) to nu(parallel to) = 1/4 above p(c). Other critical exponents of the diode-resistor problem on the Cayley tree are gamma = 0 and nu(perpendicular to) = 0, suggesting that nu(perpendicular to)/nu(parallel to) --> 0 when d --> infinity. Simulation results in finite dimensions 2 less than or equal to d less than or equal to 5 are also presented.