Correlations of a bound interface over a random substrate

The correlation function of a one-dimensional interface over a random substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo simulation. It is found that the height correlation 〈h<Subscript>i</Subscript>;h<Subscript>i+j</Subscript> 〉, averaged over the substrate disorder, fits a form $ae^{-(j/b)^c}$ to a surprising precision in the full range of j where the correlation is non-negligible. The exponent c increases from 1.0 to 1.5 when the interface tension is taken larger and larger. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006