{
  "id": "cond-mat/0408048",
  "version": "v1",
  "published": "2004-08-02T22:39:47.000Z",
  "updated": "2004-08-02T22:39:47.000Z",
  "title": "Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets",
  "authors": [
    "Leon Balents",
    "Pierre Le Doussal"
  ],
  "doi": "10.1016/j.aop.2004.10.001",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.soft",
    "cond-mat.stat-mech"
  ],
  "abstract": "Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects, described by a displacement field u and internal dimension d, pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T=0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative *thermal boundary layer* (TBL) in the (running) effective action Gamma[u] at T>0 for which we find a consistent scaling ansatz to all orders. The TBL resolves the singularities of the T=0 theory and contains rare droplet physics. The formal structure of this TBL is explored around d=4 using a one loop Wilson RG. A more systematic Exact RG (ERG) method is employed and tested on d=0 models. There we obtain precise relations between TBL quantities and droplet probabilities which are checked against exact results. We illustrate how the TBL scaling remains consistent to all orders in higher d using the ERG and how droplet picture results can be retrieved. Finally, we solve for d=0,N=1 the formidable \"matching problem\" of how this T>0 TBL recovers a critical T=0 field theory. We thereby obtain the beta-function at T=0, *all ambiguities removed*, displayed here up to four loops. A discussion of d>4 case and an exact solution at large d are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-02T22:39:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "field theory",
      "pinned elastic systems",
      "thermal fluctuations",
      "rare events",
      "contains rare droplet physics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}