Correlation functions near Modulated and Rough Surfaces

Details Correlation functions near Modulated and Rough Surfaces Correlation functions near Modulated and Rough Surfaces

2001-10-25

arxiv.org/abs/cond-mat/0110532v1

Physics

Condensed Matter

Statistical Mechanics

31 pages, 2 figures

Scientific paper

10.1103/PhysRevE.65.046121

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near surface correlations can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent $\zeta$. By combining this perturbative calculation in height deformations with the field-theoretic renormalization group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough $\zeta$ can lead to novel surface critical behavior. We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.

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