{
  "id": "cond-mat/0603151",
  "version": "v2",
  "published": "2006-03-07T14:43:40.000Z",
  "updated": "2006-08-09T11:20:12.000Z",
  "title": "Directed percolation with incubation times",
  "authors": [
    "Andrea Jimenez-Dalmaroni"
  ],
  "comment": "17 pages, 7 figures. v.2: minor corrections",
  "journal": "Phys. Rev. E 74, 011123 (2006)",
  "doi": "10.1103/PhysRevE.74.011123",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Levy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Levy parameter.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-09T11:20:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed percolation",
      "incubation times",
      "long-range temporal diffusion",
      "critical exponents",
      "scaling relation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}