{
  "id": "2307.01801",
  "version": "v1",
  "published": "2023-07-04T16:10:19.000Z",
  "updated": "2023-07-04T16:10:19.000Z",
  "title": "From stretched exponential to power-law: crossover of relaxation in a simple model",
  "authors": [
    "Sukanta Mukherjee",
    "Puneet Pareek",
    "Mustansir Barma",
    "Saroj Kumar Nandi"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "The autocorrelation function in many complex systems shows a crossover of its decay: from stretched exponential relaxation (SER) at short times to power-law at long times. Study of the mechanisms leading to such multiple relaxation patterns are rare. Additionally, the inherent complexity of these systems makes it hard to understand the underlying mechanism leading to the crossover. Here we develop a simple one-dimensional spin model, which we call a Domain Wall to Doublon (DWD) model, that shows such a crossover. The nature of the excitations governing the relaxation dynamics changes with temperature. The relevant excitations are domain walls (DWs) and bound pairs of DWs, which we term ``doublons''. The diffusive motions of the DWs govern the relaxation at short times, whereas the diffusive motions of the doublons give the decay at long times. This crossover of relaxation mechanisms leads to the crossover, from SER to power-law, in the decay pattern of the autocorrelation functions. We augment our numerical results by analytical derivations of the relaxation forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-04T16:10:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stretched exponential",
      "simple model",
      "domain wall",
      "simple one-dimensional spin model",
      "long times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}