{
  "id": "2209.09689",
  "version": "v1",
  "published": "2022-09-20T12:51:56.000Z",
  "updated": "2022-09-20T12:51:56.000Z",
  "title": "Stochastic equations and dynamics beyond mean-field theory",
  "authors": [
    "Tommaso Rizzo"
  ],
  "comment": "Contribution to the edited volume \"Spin Glass Theory and Far Beyond - Replica Symmetry Breaking after 40 years\", World Scientific",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition are described in the $\\beta$ regime by dynamical stochastic equations. The quantitative parameters of the dynamical stochastic equations have been computed analytically on the 3-spin Bethe lattice Spin-Glass by means of the (static) cavity method and the equations have been solved numerically. The resulting parameter-free dynamical predictions are shown here to be in excellent agreement with numerical simulation data for the correlation and its fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-20T12:51:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field theory",
      "dynamical stochastic equations",
      "bethe lattice spin-glass",
      "spin-glass models",
      "numerical simulation data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}