{
  "id": "1609.07084",
  "version": "v1",
  "published": "2016-09-22T17:47:34.000Z",
  "updated": "2016-09-22T17:47:34.000Z",
  "title": "Average Free-Energy of Directed Polymers and Interfaces in Random Media",
  "authors": [
    "R. Acosta Diaz",
    "C. D. Rodríguez-Camargo",
    "N. F. Svaiter"
  ],
  "comment": "19 pages. arXiv admin note: text overlap with arXiv:1603.05919",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We consider first the field theory formulation for a directed polymer in the presence of a quenched disorder. To obtain the average free-energy of this system we use the distributional zeta-function method. The distributional zeta-function is a complex function whose derivative at the origin yields the average free-energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which can not be written as a series of the integer moments, but can be made as small as desired. Using the saddle-point equations of the model, and the replica symmetry ansatz, we obtain that the numbers of terms in the series representation for the average free-energy depends on the temperature of the system. Next, the field theory formulation of an interface in a quenched random potential is considered. Also using the results obtained from the distributional zeta-function method, the average free-energy of this system is presented. The $k$-th term of the series that defines the average free-energy represents an Euclidean field theory for a $k$-component Gaussian scalar field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-22T17:47:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed polymer",
      "random media",
      "distributional zeta-function method",
      "field theory formulation",
      "component gaussian scalar field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}