Modified critical correlations close to modulated and rough surfaces

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be m easured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. Th e results, combined with a renormalization group around four dimensions, ar e 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.