{
  "id": "cond-mat/0110532",
  "version": "v1",
  "published": "2001-10-25T02:07:01.000Z",
  "updated": "2001-10-25T02:07:01.000Z",
  "title": "Correlation functions near Modulated and Rough Surfaces",
  "authors": [
    "Andreas Hanke",
    "Mehran Kardar"
  ],
  "comment": "31 pages, 2 figures",
  "doi": "10.1103/PhysRevE.65.046121",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-25T02:07:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "correlation functions",
      "self-affinely rough surface",
      "flat surface",
      "field-theoretic renormalization group approach",
      "perturbative calculation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}