2001/10/25 by Andreas Hanke, Mehran Kardar
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.046121
31 pages, 2 figures
arxiv created 2001/10/25 · openalex publication_date 2002/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a different surface critical behavior. We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.