G. Giugliarelli et Al. Stella, SOLID-ON-SOLID MODEL FOR ADSORPTION ON SELF-AFFINE SUBSTRATE - A TRANSFER-MATRIX APPROACH, Physica. A, 212(1-2), 1994, pp. 12-25
We study a d = 2 discrete solid-on-solid model of complete wetting of
a rough substrate with random self-affine boundary, having roughness e
xponent 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) less than or equal to 1/2 the same wett
ing exponent psi = 1/3 as for flat substrate is obtained for the depen
dence of the coverage, theta, on the chemical potential, h (theta simi
lar to h(-psi) for h --> 0). The expected existence of a zero temperat
ure 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 conv
ergence to asymptotics.