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 for h → 0). 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. PACS numbers: 68.45, 68.55.Jk, 05.40 (Submitted for publication to PHYSICA A) Email: [email protected], [email protected]