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 ${\zeta }_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For ${\zeta }_s\le 1/2$ the same wetting exponent $\psi =1/3$ as for flat substrate is obtained for the dependence of the coverage, $\theta$, on the chemical potential, $h$ ($\theta \sim h^{-\psi }$ for $h\to 0$). 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.

Standard TeX, 13 pages. 5 PostScript figures available on request. Preprint UDPHIR 94/04/GG

Cited by in corpus (3)

• Stochastic Growth Equations and Reparametrization Invariance
• Discontinuous Interface Depinning from a Rough Wall
• Reentrant Wetting Transition of a Rough Wall