{
  "id": "1006.0875",
  "version": "v1",
  "published": "2010-06-04T12:02:08.000Z",
  "updated": "2010-06-04T12:02:08.000Z",
  "title": "Localization for (1+1)-dimensional pinning models with $(\\nabla + Δ)$-interaction",
  "authors": [
    "Martin Borecki",
    "Francesco Caravenna"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the localization/delocalization phase transition in a class of directed models for a homogeneous linear chain attracted to a defect line. The self-interaction of the chain is of mixed gradient and Laplacian kind, whereas the attraction to the defect line is of $\\delta$-pinning type, with strength $\\epsilon \\geq 0$. It is known that, when the self-interaction is purely Laplacian, such models undergo a non-trivial phase transition: to localize the chain at the defect line, the reward $\\epsilon$ must be greater than a strictly positive critical threshold $\\epsilon_c > 0$. On the other hand, when the self-interaction is purely gradient, it is known that the transition is trivial: an arbitrarily small reward $\\epsilon > 0$ is sufficient to localize the chain at the defect line ($\\epsilon_c = 0$). In this note we show that in the mixed gradient and Laplacian case, under minimal assumptions on the interaction potentials, the transition is always trivial, that is $\\epsilon_c = 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-04T12:02:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B41",
      "60J05"
    ],
    "keywords": [
      "defect line",
      "pinning models",
      "localization/delocalization phase transition",
      "self-interaction",
      "mixed gradient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0875B"
    }
  }
}