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 ζs. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For ζs ≤ 1/2 the same wetting exponent ψ = 1/3 as for flat substrate is obtained for the dependence of the coverage, θ, on the chemical potential, h (θ h-ψ for h → O). The expected existence of a zero temperature fixed point, leading to ψ = ζs/(2−ζs) for ζs > 1/2, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.