UDPHIR 94/04/GG
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title: "SOLID ON SOLID MODEL OF ADSORPTION ON SELF-AFFINE SUBSTRATE:
A TRANSFER MATRIX APPROACH"
Authors: G.Giugliarelli and A.L.Stella
Comments: 13 pages TeX, 5 figures, published on Physica A, 212 12-25 (1994)
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 $\zeta_s\leq 1/2$ 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.