{
  "id": "1305.2070",
  "version": "v3",
  "published": "2013-05-09T12:31:39.000Z",
  "updated": "2013-09-25T15:35:53.000Z",
  "title": "Replica-symmetry-breaking transitions and off-equilibrium dynamics",
  "authors": [
    "Tommaso Rizzo"
  ],
  "comment": "16 pages, final version published on PRE",
  "journal": "Phys. Rev. E 88, 032135 (2013)",
  "doi": "10.1103/PhysRevE.88.032135",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "I consider branches of Replica-Symmetry-Breaking (RSB) solutions in Glassy systems that display a dynamical transition at a temperature $T_d$ characterized by a Mode-Coupling-Theory dynamical behavior. Below $T_d$ these branches of solutions are considered to be relevant to the complexity and to off-equilibrium dynamics. Under general assumptions I argue that near $T_d$ it is not possible to stabilize the one-step (1RSB) solution beyond the marginal point by making a full RSB (FRSB) ansatz. However, depending on the model, it may exist a temperature $T_*$ strictly lower than $T_d$ below which the 1RSB branch can be continued to a FRSB branch. Such a temperature certainly exists for models that display the so-called Gardner transition and in this case $T_G<T_*<T_d$. An analytical study in the context of the truncated model reveals that the FRSB branch of solutions below $T_*$ is characterized by a two plateau structure and it ends where the first plateau disappears. These general features are confirmed in the context of the Ising $p$-spin with $p=3$ by means of a numerical solution of the FRSB equations. The results are discussed in connection with off-equilibrium dynamics within Cugliandolo-Kurchan theory. In this context I assume that the RSB solution relevant for off-equilibrium dynamics is the 1RBS marginal solution in the whole range $(T_*,T_d)$ and it is the end-point of the FRSB branch for $T<T_*$. Remarkably under these assumptions it can be argued that $T_*$ marks a qualitative change in off-equilibrium dynamics in the sense that the decay of various dynamical quantities changes from power-law to logarithmic.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-25T15:35:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "64.70.qj",
      "64.60.Ht",
      "75.10.Nr"
    ],
    "keywords": [
      "off-equilibrium dynamics",
      "replica-symmetry-breaking transitions",
      "frsb branch",
      "temperature",
      "first plateau disappears"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2013,
      "month": "Sep",
      "volume": 88,
      "number": 3,
      "pages": "032135"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvE..88c2135R"
    }
  }
}