Solid-on-solid Model For Adsorption On Self-affine Substrate - A Transfer-matrix Approach

We study a d = 2 discrete solid-on-solid model of complete wetting of a rough substrate with random self-affine boundary, having roughness exponent zeta(s). A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For zeta(s) less than or equal to 1/2 the same wetting exponent psi = 1/3 as for flat substrate is obtained for the dependence of the coverage, theta, on the chemical potential, h (theta similar to h(-psi) for h --> 0). The expected existence of a zero temperature fixed point, leading to psi = zeta(s)/(2 - zeta(s)) for zeta(s) > 1/2, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.