Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affine rough surface. We find that a large enough roughness exponent can modify surface critical behavior.
Hanke, Andreas, and Mehran Kardar. “Modified Critical Correlations Close to Modulated and Rough Surfaces.” Physical Review Letters, vol. 86, no. 20, American Physical Society, May 2001, pp. 4596–99, doi:10.1103/PhysRevLett.86.4596.
Physical Review Letters