Solid--on--Solid Model for Adsorption on Self--Affine Substrate: A Transfer Matrix Approach

Abstract

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 $ζ_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For $ζ_s\leq 1/2$ the same wetting exponent $ψ=1/3$ as for flat substrate is obtained for the dependence of the coverage, $θ$, on the chemical potential, $h$ ($θ\sim h^{-ψ}$ for $h\to 0$). The expected existence of a zero temperature fixed point, leading to $ψ=ζ_s /(2-ζ_s)$ for $ζ_s>1/2$, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.