Scaling in the solid-on-solid interfaces

Abstract

The explicit forms of the density-density correlation function H( Delta x,z1,z2) for the transverse separation Delta x approximately W2, where W is the interface thickness, are obtained in the two-dimensional solid-on-solid model in two different asymptotic cases of a finite system in a vanishing external field. The results support the Weeks (1984) scaling hypothesis. The form of Hs ( Delta x/ xi perpendicular to ,z1/W,z2/W) depends on the geometry of the system. The relation between W and transverse correlation length xi perpendicular to has the same form in different external conditions localising the interface in solid-on-solid and capillary-wave models.