{
  "id": "2407.08502",
  "version": "v1",
  "published": "2024-07-11T13:37:15.000Z",
  "updated": "2024-07-11T13:37:15.000Z",
  "title": "General properties of the response function in a class of solvable non-equilibrium models",
  "authors": [
    "Federico Corberi",
    "Luca Smaldone"
  ],
  "comment": "12 pages, 3 figures. Submitted to Journal of Physics A: Mathematical and Theoretical",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the non-equilibrium response function $R_{ij}(t,t')$, namely the variation of the local magnetization $\\langle S_i(t)\\rangle$ on site $i$ at time $t$ as an effect of a perturbation applied at the earlier time $t'$ on site $j$, in a class of solvable spin models characterized by the vanishing of the so-called {\\it asymmetry}. This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio $X_{ij}(t,t')=\\beta R_{ij}/(\\partial G_{ij}/\\partial t')$, where $G_{ij}(t,t')=\\langle S_i(t)S_j(t')\\rangle$ is the spin-spin correlation function and $\\beta$ is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal form$X_{ii}(t,t') = (t+t')/(2t)$, whereas $\\lim _{t\\to \\infty}X_{ij}(t,t')=1/2$ for any $ij$ couple. The specific case of voter models with long-range interactions is thoroughly discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-11T13:37:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "solvable non-equilibrium models",
      "general properties",
      "voter model",
      "non-equilibrium response function",
      "spin-spin correlation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}